Question

1. prove that △abe ~ △cde in a trapezoid where ab || cd and diagonals intersect at e. which reasoning is correct? a. sss similarity criterion b. aa similarity criterion c. hl congruence criterion d. sss congruence criterion 11 in triangle △abc, ab = 8 cm, bc = 10 cm, and ac = 12 cm. in triangle △def, de = 16 cm and ef = 20 cm. what is the

Explanation:

Step1: Identify parallel - sides property

Since $\overline{AB}\parallel\overline{CD}$ in the trapezoid, we can find equal angles. The alternate - interior angles are equal. Let $\angle BAE=\angle DCE$ and $\angle ABE=\angle CDE$ because of the parallel lines $\overline{AB}$ and $\overline{CD}$ and the transversals formed by the diagonals.

Step2: Recall similarity criterion

The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar. In $\triangle ABE$ and $\triangle CDE$, we have two pairs of equal angles as identified in Step 1.

Answer:

b. AA Similarity Criterion