Question

question 3 of 10
based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why \\( \triangle c d e \cong \triangle o p q \\) ?
check all that apply.
a. ll
b. aas
c. sas
d. ha
e. hl
f. asa

Explanation:

Step1: Analyze AAS (Angle - Angle - Side)

In right - angled triangles \(\triangle CDE\) and \(\triangle OPQ\), we have two angles (the right angles and the other marked equal angles) and a non - included side (the equal sides \(CE = OQ\)). AAS (Angle - Angle - Side) congruence theorem states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Step2: Analyze HA (Hypotenuse - Angle)

For right - angled triangles, HA (Hypotenuse - Angle) is a valid congruence criterion. Here, the hypotenuse \(CE = OQ\) (given as equal in the diagram) and an acute angle (the non - right angles which are equal) satisfy the HA criterion.

Answer:

B. AAS, D. HA