Question

what else is needed to prove these triangles congruent using the hl theorem? both ∠abc and ∠dcb need to equal 90°. ∠a≅∠d. nothing else is needed to use the hl theorem.

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

The HL theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.

Step2: Analyze given information

We know that we have two triangles formed within the figure. To use the HL theorem, we need to have right - triangles.

Step3: Determine missing condition

Since the HL theorem applies only to right - triangles, we need to have right - angles in the triangles. In the context of the two triangles formed by the diagonal of the figure, we need $\angle ABC$ and $\angle DCB$ to be $90^{\circ}$ so that we can apply the HL theorem.

Answer:

Both $\angle ABC$ and $\angle DCB$ need to equal $90^{\circ}$.