Question

based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why △cde≅△opq? check all that apply. a. aas b. la c. ll d. asa e. hl f. sas

Explanation:

Step1: Analyze right - angled triangles

We have two right - angled triangles $\triangle CDE$ and $\triangle OPQ$. The right angles are $\angle C=\angle O = 90^{\circ}$. There are marks indicating equal sides and equal non - right angles.

Step2: Evaluate AAS

AAS (Angle - Angle - Side) states that 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. From the diagram, we can see two non - right angles and a non - included side are equal, so AAS could apply.

Step3: Evaluate LA

LA (Leg - Angle) for right - angled triangles. If a leg and an acute angle of one right - angled triangle are congruent to a leg and the corresponding acute angle of another right - angled triangle, the triangles are congruent. This can be applied as we have a leg and an acute angle equal in the two right - angled triangles.

Step4: Evaluate LL

LL (Leg - Leg) requires that the two legs of one right - angled triangle are congruent to the two legs of another right - angled triangle. There is no indication that both legs are equal, so LL does not apply.

Step5: Evaluate ASA

ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. There is no indication that the included side between the angles is congruent, so ASA does not apply.

Step6: Evaluate HL

HL (Hypotenuse - Leg) requires the hypotenuse and a leg of one right - angled triangle to be congruent to the hypotenuse and the corresponding leg of another right - angled triangle. There is no indication about the hypotenuse, so HL does not apply.

Step7: Evaluate SAS

SAS (Side - Angle - Side) requires two sides and the included angle to be congruent. There is no indication that the included angle between the sides is congruent, so SAS does not apply.

Answer:

A. AAS
B. LA