Discussion
ΔABC and ΔADB are on the common base AB and on the same side of AB. DA⊥AB, CB⊥AB and AC = BD. Which of the following is true ?
Answer: C
The true statement is ΔABC ≅ ΔBAD.
Since DA ⊥ AB and CB ⊥ AB, both triangles are right-angled: ΔABC at B and ΔBAD at A. Their hypotenuses are equal (AC = BD) and they share the side AB. By the RHS congruence rule the triangles are congruent.
The correspondence must match equal parts: the right angle B of ΔABC goes to the right angle A, the vertex A goes to B, and C goes to D. So A ↔ B, B ↔ A, C ↔ D, written ΔABC ≅ ΔBAD. The other orderings pair the right angles or the hypotenuses wrongly, even though they name the same two triangles.
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