- ASSS
- BSAS
- CASA
- DRHS
Step-by-Step Solution
The ticks show and , and the arcs show . The marked angle lies between the two marked sides, so the rule is SAS.
Answer: B) SAS
Look at the matching marks on the two triangles. Which congruence rule shows that △ABC ≅ △PQR?
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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