Question

3.2.3 quiz: proving right triangle congruence
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why \\( \triangle cde \cong \triangle opq \\)?
check all that apply.
a. hl
b. sas
c. la
d. asa
e. ll
f. aas

Explanation:

• HL (Hypotenuse - Leg): If the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, the triangles are congruent. In right - triangles \(\triangle CDE\) and \(\triangle OPQ\), if we assume the marked segments (one leg and the hypotenuse) are congruent (from the diagram's markings), HL can be used.
• LA (Leg - Angle): If a leg and an acute angle of one right - triangle are congruent to the corresponding leg and acute angle of another right - triangle, the triangles are congruent. Here, we have a right angle (\(90^{\circ}\)), a leg (marked in the diagram), and an acute angle (marked in the diagram) for both triangles.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent. We have two angles (right angle and the marked acute angle) and a side (marked leg) for both triangles.

Answer:

A. HL, C. LA, F. AAS