Question

triangles adc and bcd are shown below. which additional fact is needed to prove △adc≅△bcd by the hypotenuse - leg theorem? ∠a = ∠b = 45° ac≅bd ad≅bc ∠a>∠b

Explanation:

Step1: Recall hypotenuse - leg theorem

The hypotenuse - leg (HL) theorem states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent. In right - triangles $\triangle ADC$ and $\triangle BCD$, $\angle ADC=\angle BCD = 90^{\circ}$ and $DC$ is a common side (leg).

Step2: Identify the required congruence

We need the hypotenuses of the two right - triangles to be congruent. The hypotenuse of $\triangle ADC$ is $AC$ and the hypotenuse of $\triangle BCD$ is $BD$. So, we need $AC\cong BD$.

Answer:

$AC\cong BD$