- A80°
- B40°
- C72°
- D140°
Step-by-Step Solution
(SSS, common), so . In , and by CPCT , so .
Answer: A) 80°
ABCD is a kite with AB = AD and CB = CD (tick marks), and diagonal AC splits it into two triangles. ∠DAC = 32° and ∠ABC = 108°. Find ∠BCD.
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: Why SSA is not a valid congruence criterion
If you give two sides and an angle that is NOT between them, you can sometimes draw two different triangles with those measurements. The angle-and-opposite-side combination doesn't pin down the triangle uniquely.
The ONE case it works is when the angle is a RIGHT angle and the side opposite is the hypotenuse — that's exactly the RHS criterion. So RHS is essentially 'SSA but only for right triangles, and the side has to be the hypotenuse'.
**Bottom line**: Always check the angle is INCLUDED between the two sides before quoting SAS. Otherwise you've made the classic SSA mistake.
The ONE case it works is when the angle is a RIGHT angle and the side opposite is the hypotenuse — that's exactly the RHS criterion. So RHS is essentially 'SSA but only for right triangles, and the side has to be the hypotenuse'.
**Bottom line**: Always check the angle is INCLUDED between the two sides before quoting SAS. Otherwise you've made the classic SSA mistake.
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