Consider two triangles, △ABC and △DEF. It is stated that these two triangles are congruent to each other, which is denoted as △ABC≅△DEF and ∠A=50°, what is the measure of ∠D?

Correct — B. In a congruence statement the letter order is the matching.

Read △ABC ≅ △DEF position by position:
A ↔ D, B ↔ E, C ↔ F

Corresponding parts of congruent triangles are equal (CPCT):
∠D = ∠A = 50° → option (b)

Why the others are wrong

• (a)
  40° — 40° is the complement of 50° (90° − 50°). Congruence copies each angle exactly, and nothing in the stem makes ∠A and ∠D add to 90°.
• (c)
  60° — 60° differs from the given ∠A = 50°, and congruence allows no change between matched angles. 60° is each angle of an equilateral triangle, which the stem never describes.
• (d)
  130° — 130° is the supplement of 50° (180° − 50°), the exterior angle at A. Congruent triangles match interior angles, so ∠D = 50°.

Two triangles are congruent when one fits exactly on the other: all three sides and all three angles match.

The symbol ≅ carries the matching in its letter order. △ABC ≅ △DEF pairs the first letters (A, D), the second (B, E) and the third (C, F).

Once the triangles are congruent, every pair of corresponding parts is equal. That is what CPCT means.

Key facts

• In △ABC ≅ △DEF the vertices pair by position: A with D, B with E, C with F.
• CPCT: corresponding parts of congruent triangles are equal.
• SSS, SAS, ASA, AAS and RHS prove congruence, while AAA proves similarity.

Common traps

• Matching vertices by alphabet or by a drawing instead of by their order in the ≅ statement.
• Treating 50° as a starting point for a calculation and giving its complement or supplement.

No directly related past PYQ was found.