Question

overlapping triangles. which of the following relationships proves why △adc and △bcd are congruent? asa hl saa sas

Explanation:

Step1: Identify common side

In \(\triangle ADC\) and \(\triangle BCD\), \(DC = CD\) (common - side).

Step2: Identify right - angles

\(\angle ADC=\angle BCD = 90^{\circ}\) (given right - angles).

Step3: Apply congruence criterion

We have a right - angle, a common side (hypotenuse for right - triangles) and we can consider the right - angle and the hypotenuse relationship. The Hypotenuse - Leg (HL) congruence criterion states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, the two right - triangles are congruent. Here, the hypotenuse \(DC\) is common to both right - triangles \(\triangle ADC\) and \(\triangle BCD\).

Answer:

HL