- A50°
- B40°
- C130°
- D90°
Step-by-Step Solution
By CPCT, corresponding parts of congruent triangles are equal. ∠A corresponds to ∠D, so ∠D = 50°.
Answer: A) 50°
If ΔABC ≅ ΔDEF and ∠A = 50°, what is ∠D?
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: How to write a 2-column proof
Indian textbooks prefer paragraph-style proofs, but the LOGIC is the same. The structure:
**Given**: list what's stated in the problem.
**To prove**: the goal statement.
**Proof**: a sequence of facts, each justified.
Example: In ΔABC, AB = AC. Prove ∠B = ∠C.
Given: AB = AC.
To prove: ∠B = ∠C.
Construction: Draw AD, the angle bisector of ∠A, meeting BC at D.
Proof: In ΔABD and ΔACD,
AB = AC (given)
∠BAD = ∠CAD (construction)
AD = AD (common)
∴ ΔABD ≅ ΔACD (SAS)
∴ ∠B = ∠C (CPCT). ∎
**Given**: list what's stated in the problem.
**To prove**: the goal statement.
**Proof**: a sequence of facts, each justified.
Example: In ΔABC, AB = AC. Prove ∠B = ∠C.
Given: AB = AC.
To prove: ∠B = ∠C.
Construction: Draw AD, the angle bisector of ∠A, meeting BC at D.
Proof: In ΔABD and ΔACD,
AB = AC (given)
∠BAD = ∠CAD (construction)
AD = AD (common)
∴ ΔABD ≅ ΔACD (SAS)
∴ ∠B = ∠C (CPCT). ∎
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