ΔABC and ΔDEF are two triangles such that ΔABC≅ΔFDE. If AB=17 cm, ∠B=52° and ∠A=95°, then which of the following options is true?

Correct — D. The congruence is written ΔABC≅ΔFDE, so letters pair by position: A ↔ F, B ↔ D, C ↔ E.

Third angle: ∠C = 180° − 95° − 52° = 33°

Side AB ↔ FD, so DF = 17 cm
Angle ∠C ↔ ∠E, so ∠E = 33°
Check the rest: ∠F = ∠A = 95° and ∠D = ∠B = 52°

DF = 17 cm and ∠E = 33° → option (d)

Why the others are wrong

• (a)
  DE=17 cm,∠E=33° — ∠E = 33° is right, but DE pairs with BC, not AB. The stem gives no length for BC.
• (b)
  DE=17 cm,∠F=33° — Both parts fail. DE pairs with BC, and ∠F matches ∠A, which is 95°, not 33°.
• (c)
  DF=17 cm,∠D=33° — DF = 17 cm is right, but ∠D matches ∠B, which is 52°. The 33° angle sits at E, the partner of C.

The position of each letter in a congruence statement fixes the correspondence. In ΔABC ≅ ΔFDE the first letters pair (A, F), then the second (B, D), then the third (C, E).

A side is matched through both endpoints, so AB ↔ FD. An angle is matched through its vertex, so ∠C ↔ ∠E.

The missing angle ∠C comes from the angle sum, then moves to its partner E.

Key facts

• ΔABC ≅ ΔFDE pairs A with F, B with D and C with E.
• The side pairs are AB ↔ FD, BC ↔ DE and CA ↔ EF.
• ∠C = 180° − 95° − 52° = 33°, so ∠E = 33°.

Common traps

• Matching by the name ΔDEF instead of the written order ΔFDE
• Treating DF and FD as different sides, when they are the same segment
• Finding ∠C = 33° and then placing it at F, the first letter, instead of at E

No directly related past PYQ was found.