Angle-side relationships in triangles

key notes :

๐Ÿ‘‰ In a triangle, angles and sides are related โ€”
๐Ÿ“ The longer side is opposite the larger angle, and
๐Ÿ“ The shorter side is opposite the smaller angle.

โžก๏ธ Bigger Angle โ†’ Longer Opposite Side
โžก๏ธ Smaller Angle โ†’ Shorter Opposite Side


๐Ÿงฉ If you know the angle measures, you can order the sides easily!
Example:
If โˆ A > โˆ B > โˆ C
๐Ÿ‘‰ Then side BC > AC > AB

And vice versa:
If side BC > AC > AB
๐Ÿ‘‰ Then โˆ A > โˆ B > โˆ C


๐Ÿง  The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

โœ… a + b > c
โœ… a + c > b
โœ… b + c > a

๐Ÿšซ If this rule is not true, a triangle cannot be formed!


If one side of a triangle is longer, then the angle opposite that side is larger.
Example:
If side AB > side AC
๐Ÿ‘‰ Then โˆ C > โˆ B


In an isosceles triangle,
โœจ Two sides are equal,
โœจ The angles opposite those sides are also equal.

๐Ÿ“ Example: If AB = AC, then โˆ B = โˆ C


  • Used in geometry proofs and construction problems.
  • Helps in ranking sides or angles by size.
  • Important in real-life applications like design, construction, and navigation.

RelationRule
Larger Angle โ†” Longer Sideโœ…
Smaller Angle โ†” Shorter Sideโœ…
Equal Sides โ†” Equal Anglesโœ…
a + b > cTriangle can exist โœ…

In โ–ณABC,
โˆ A = 40ยฐ, โˆ B = 70ยฐ, โˆ C = 70ยฐ
๐Ÿ‘‰ Side a (BC) is shortest ๐Ÿชถ
๐Ÿ‘‰ Sides b (AC) and c (AB) are equal and longer ๐Ÿ—๏ธ


Angles and sides in a triangle always “balance” each other!
The bigger the angle, the longer the opposite side โ€”
Thatโ€™s the beauty of triangles! ๐Ÿ’–๐Ÿ”บ

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