- ASSS
- BSAS
- CRHS
- DAAA
Step-by-Step Solution
PQ = PR (given), ∠QPS = ∠RPS (PS bisects ∠P), PS = PS (common). Two sides and the included angle → SAS.
Answer: B) SAS
In ΔPQR, the bisector of ∠P meets QR at S, and PQ = PR. State the criterion proving ΔPQS ≅ ΔPRS.
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: Isosceles triangle properties
**Theorem**: Angles opposite equal sides of an isosceles triangle are equal.
In ΔABC if AB = AC, then ∠B = ∠C.
**Proof sketch**: Drop a median (or angle bisector) from A to BC, meeting at D.
- AB = AC (given), AD = AD (common), BD = DC (median).
- By SSS, ΔABD ≅ ΔACD.
- By CPCT, ∠B = ∠C. ✓
**Converse**: Sides opposite equal angles are equal. (∠B = ∠C → AB = AC.)
In ΔABC if AB = AC, then ∠B = ∠C.
**Proof sketch**: Drop a median (or angle bisector) from A to BC, meeting at D.
- AB = AC (given), AD = AD (common), BD = DC (median).
- By SSS, ΔABD ≅ ΔACD.
- By CPCT, ∠B = ∠C. ✓
**Converse**: Sides opposite equal angles are equal. (∠B = ∠C → AB = AC.)
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