{"id":220,"date":"2022-04-13T08:45:00","date_gmt":"2022-04-13T08:45:00","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=220"},"modified":"2025-12-19T06:18:16","modified_gmt":"2025-12-19T06:18:16","slug":"m-2-construct-an-angle-bisector","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/m-2-construct-an-angle-bisector\/","title":{"rendered":"M.2 Construct an angle bisector"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Construct an angle bisector<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/i.ytimg.com\/vi\/c2x0NATrBIY\/maxresdefault.jpg?utm_source=chatgpt.com\" alt=\"https:\/\/i.ytimg.com\/vi\/c2x0NATrBIY\/maxresdefault.jpg?utm_source=chatgpt.com\" style=\"width:423px;height:auto\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.mathopenref.com\/images\/constructions\/constbisectangle\/proof.png?utm_source=chatgpt.com\" alt=\"https:\/\/www.mathopenref.com\/images\/constructions\/constbisectangle\/proof.png?utm_source=chatgpt.com\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 What is an Angle Bisector?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>An <strong>angle bisector<\/strong> is a line or ray that <strong>divides an angle into two equal angles<\/strong>.<\/li>\n\n\n\n<li>If \u2220ABC is an angle, its bisector splits it into <strong>two congruent angles<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 Tools Required<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u270f\ufe0f Pencil<\/li>\n\n\n\n<li>\ud83d\udccf Ruler (straightedge)<\/li>\n\n\n\n<li>\ud83e\udded Compass<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 Steps to Construct an Angle Bisector<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Draw the given angle<\/strong> \u2220ABC.<\/li>\n\n\n\n<li>Place the <strong>compass at the vertex (B)<\/strong> and draw an arc that cuts both arms of the angle at points <strong>P<\/strong> and <strong>Q<\/strong>.<\/li>\n\n\n\n<li>Without changing the compass width, place it at <strong>P<\/strong> and draw an arc inside the angle.<\/li>\n\n\n\n<li>Again, with the same width, place the compass at <strong>Q<\/strong> and draw another arc to <strong>intersect the previous arc<\/strong> at point <strong>R<\/strong>.<\/li>\n\n\n\n<li>Use a ruler to <strong>join B and R<\/strong>.<\/li>\n\n\n\n<li><strong>BR is the angle bisector<\/strong> of \u2220ABC.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 Important Properties<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The angle bisector <strong>divides the angle into two equal parts<\/strong>.<\/li>\n\n\n\n<li>Every angle has <strong>one and only one bisector<\/strong>.<\/li>\n\n\n\n<li>Points on the angle bisector are <strong>equidistant from both arms<\/strong> of the angle.<\/li>\n\n\n\n<li>Angle bisectors are used in <strong>triangle constructions<\/strong>, especially for <strong>incentres<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 Key Tips for Exams \ud83d\udcdd<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always <strong>show construction arcs clearly<\/strong>.<\/li>\n\n\n\n<li>Do <strong>not erase arcs<\/strong> unless instructed.<\/li>\n\n\n\n<li>Label points neatly for clarity.<\/li>\n\n\n\n<li>Mention the <strong>steps in correct order<\/strong> in construction questions.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udd39 Real-Life Application<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Used in <strong>architecture and engineering<\/strong> to divide angles accurately.<\/li>\n\n\n\n<li>Helps in <strong>design symmetry<\/strong> and precise measurements.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f1cccc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>The diagram below shows a nearly completed construction of the bisector of \u2220A. Complete the construction.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"734\" height=\"517\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-4.png\" alt=\"\" class=\"wp-image-11976\" style=\"aspect-ratio:1.4197292069632494;width:505px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-4.png 734w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-4-300x211.png 300w\" sizes=\"auto, (max-width: 734px) 100vw, 734px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>Part of the construction was done for you. Here are the steps to create this part of the construction.<\/p>\n\n\n\n<p><strong>Start with the objects in the diagram below.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"285\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115455.171.png\" alt=\"\" class=\"wp-image-11977\" style=\"aspect-ratio:1.080701754385965;width:323px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115455.171.png 308w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115455.171-300x278.png 300w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><em>Draw&nbsp;a circle with radius&nbsp;AB&nbsp;centred at&nbsp;<\/em>A.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"406\" height=\"365\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115550.933.png\" alt=\"\" class=\"wp-image-11978\" style=\"aspect-ratio:1.1123287671232878;width:442px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115550.933.png 406w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115550.933-300x270.png 300w\" sizes=\"auto, (max-width: 406px) 100vw, 406px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the point where \u2a00A and AC intersect. Call it D.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"378\" height=\"367\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115659.608.png\" alt=\"\" class=\"wp-image-11979\" style=\"aspect-ratio:1.0299727520435968;width:382px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115659.608.png 378w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115659.608-300x291.png 300w\" sizes=\"auto, (max-width: 378px) 100vw, 378px\" \/><\/figure><\/div>\n\n\n<p>Since B and D are both on \u2a00A, AB=AD.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"392\" height=\"405\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115736.892.png\" alt=\"\" class=\"wp-image-11981\" style=\"aspect-ratio:0.9679012345679012;width:318px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115736.892.png 392w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115736.892-290x300.png 290w\" sizes=\"auto, (max-width: 392px) 100vw, 392px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a circle with radius AB centred at D.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"377\" height=\"371\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115821.997.png\" alt=\"\" class=\"wp-image-11982\" style=\"aspect-ratio:1.0161725067385445;width:399px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115821.997.png 377w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115821.997-300x295.png 300w\" sizes=\"auto, (max-width: 377px) 100vw, 377px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a circle with radius AB centred at B.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"399\" height=\"370\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115900.965.png\" alt=\"\" class=\"wp-image-11984\" style=\"aspect-ratio:1.0783783783783785;width:308px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115900.965.png 399w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T115900.965-300x278.png 300w\" sizes=\"auto, (max-width: 399px) 100vw, 399px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the point other than A where \u2a00B and \u2a00D intersect. Call it E.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"402\" height=\"381\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120017.367.png\" alt=\"\" class=\"wp-image-11985\" style=\"aspect-ratio:1.0551181102362204;width:375px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120017.367.png 402w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120017.367-300x284.png 300w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/figure><\/div>\n\n\n<p>Since A and E are both on \u2a00B, AB=BE. Since A and E are both on \u2a00D, AD=DE. Since AB=AD, AB=AD=BE=DE.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"423\" height=\"412\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120103.226.png\" alt=\"\" class=\"wp-image-11986\" style=\"aspect-ratio:1.0266990291262137;width:351px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120103.226.png 423w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120103.226-300x292.png 300w\" sizes=\"auto, (max-width: 423px) 100vw, 423px\" \/><\/figure><\/div>\n\n\n<p><strong>Complete&nbsp;the&nbsp;construction.<\/strong><\/p>\n\n\n\n<p>To complete the construction of the bisector of \u2220A, carry out the following step:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the line through A and E.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"391\" height=\"414\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120255.685.png\" alt=\"\" class=\"wp-image-11987\" style=\"aspect-ratio:0.9444444444444444;width:391px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120255.685.png 391w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120255.685-283x300.png 283w\" sizes=\"auto, (max-width: 391px) 100vw, 391px\" \/><\/figure><\/div>\n\n\n<p>Since AB=AD=BE=DE, quadrilateral ABDE is a rhombus. So, the diagonal<br>AE is the bisector of \u2220A.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"393\" height=\"425\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120405.955.png\" alt=\"\" class=\"wp-image-11988\" style=\"aspect-ratio:0.9247058823529412;width:346px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120405.955.png 393w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120405.955-277x300.png 277w\" sizes=\"auto, (max-width: 393px) 100vw, 393px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c4f0c0\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>The diagram below shows a nearly completed construction of the bisector of \u2220A. Complete the construction.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"718\" height=\"525\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-5.png\" alt=\"\" class=\"wp-image-11990\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-5.png 718w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-5-300x219.png 300w\" sizes=\"auto, (max-width: 718px) 100vw, 718px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>Part of the construction was done for you. Here are the steps to create this part of the construction.<\/p>\n\n\n\n<p><strong>Start with the objects in the diagram below.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"271\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120713.560.png\" alt=\"\" class=\"wp-image-11991\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120713.560.png 308w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120713.560-300x264.png 300w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a circle with radius AB centred at A.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"395\" height=\"343\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120832.972.png\" alt=\"\" class=\"wp-image-11993\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120832.972.png 395w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120832.972-300x261.png 300w\" sizes=\"auto, (max-width: 395px) 100vw, 395px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the point where \u2a00A and AC intersect. Call it D.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"336\" height=\"358\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120929.731.png\" alt=\"\" class=\"wp-image-11994\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120929.731.png 336w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T120929.731-282x300.png 282w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/figure><\/div>\n\n\n<p>Since B and D are both on \u2a00A, AB=AD.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"410\" height=\"376\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121034.690.png\" alt=\"\" class=\"wp-image-11995\" style=\"aspect-ratio:1.0904255319148937;width:321px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121034.690.png 410w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121034.690-300x275.png 300w\" sizes=\"auto, (max-width: 410px) 100vw, 410px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a circle with radius AB centred at D.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"416\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121153.588.png\" alt=\"\" class=\"wp-image-11996\" style=\"aspect-ratio:1.0817307692307692;width:303px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121153.588.png 450w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121153.588-300x277.png 300w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a circle with radius AB centred at B.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"467\" height=\"423\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121257.610.png\" alt=\"\" class=\"wp-image-11997\" style=\"aspect-ratio:1.1040189125295508;width:321px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121257.610.png 467w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121257.610-300x272.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the point other than A where \u2a00B and \u2a00D intersect. Call it E.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"532\" height=\"429\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121350.105.png\" alt=\"\" class=\"wp-image-11998\" style=\"aspect-ratio:1.24009324009324;width:388px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121350.105.png 532w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121350.105-300x242.png 300w\" sizes=\"auto, (max-width: 532px) 100vw, 532px\" \/><\/figure><\/div>\n\n\n<p>Since A and E are both on \u2a00B, AB=BE. Since A and E are both on \u2a00D, AD=DE. Since AB=AD, AB=AD=BE=DE.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"480\" height=\"464\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121435.926.png\" alt=\"\" class=\"wp-image-11999\" style=\"aspect-ratio:1.0344827586206897;width:277px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121435.926.png 480w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121435.926-300x290.png 300w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/figure><\/div>\n\n\n<p><strong>Complete&nbsp;the&nbsp;construction.<\/strong><\/p>\n\n\n\n<p>To complete the construction of the bisector of \u2220A, carry out the following step:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the line through A and E.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"520\" height=\"474\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121554.029.png\" alt=\"\" class=\"wp-image-12000\" style=\"aspect-ratio:1.0970464135021096;width:404px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121554.029.png 520w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121554.029-300x273.png 300w\" sizes=\"auto, (max-width: 520px) 100vw, 520px\" \/><\/figure><\/div>\n\n\n<p>Since AB=AD=BE=DE, quadrilateral ABDE is a rhombus. So, the diagonal<br>AE is the bisector of \u2220A.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"513\" height=\"486\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121634.359.png\" alt=\"\" class=\"wp-image-12001\" style=\"aspect-ratio:1.0555555555555556;width:395px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121634.359.png 513w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-05T121634.359-300x284.png 300w\" sizes=\"auto, (max-width: 513px) 100vw, 513px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-80.png\" alt=\"\" class=\"wp-image-7928\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-80.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-80-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-80-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-89.png\" alt=\"\" class=\"wp-image-7929\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-89.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-89-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-89-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Construct an angle bisector Key Notes : \ud83d\udd39 What is an Angle Bisector? \ud83d\udd39 Tools Required \ud83d\udd39 Steps to Construct an Angle Bisector \ud83d\udd39 Important Properties \ud83d\udd39 Key Tips for Exams \ud83d\udcdd \ud83d\udd39 Real-Life Application Learn with an example The diagram below shows a nearly completed construction of the bisector of \u2220A. Complete the construction.<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/m-2-construct-an-angle-bisector\/\">Continue reading <span class=\"screen-reader-text\">&#8220;M.2 Construct an angle bisector&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-220","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=220"}],"version-history":[{"count":12,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/220\/revisions"}],"predecessor-version":[{"id":18316,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/220\/revisions\/18316"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}