If ΔABC and ΔDEF are right triangles and with right angles B and E, and ∠A ≅ ∠D, then which of the following reasons explains why sin A = sin D?
a. ΔABC ~ ΔDEF by AA ~, so the corresponding sides are proportional.
b. ΔABC ≅ ΔDEF by HL Theorem, so the corresponding sides are congruent.
c. ΔABC and ΔDEF are right triangles, and all right triangles have equal trigonometric ratios.
d. The angles in both ΔABC and ΔDEF add up to 180°, which makes the two triangles have equal trigonometric ratios.
a. ΔABC ~ ΔDEF by AA ~, so the corresponding sides are proportional.
This is the correct reason why sin A = sin D. When two triangles are similar, their corresponding sides are proportional, which means that the ratios of their corresponding side lengths are equal. Since sin is a trigonometric ratio that compares the length of one side of a right triangle to the length of the hypotenuse, this ratio remains the same for corresponding angles in similar triangles. Therefore, sin A = sin D.