Question

15 multiple choice 1 point
△abd≅△cbd. name the theorem or postulate that justifies the congruence.
a
b
d
c
a. asa
b. aas
c. sas
d. hl

Explanation:

Step1: Identify given information

We have two right - angled triangles $\triangle ABD$ and $\triangle CBD$. $\angle ABD=\angle CBD = 90^{\circ}$, $\angle A=\angle C$ (marked as equal angles) and side $BD$ is common to both triangles.

Step2: Recall congruence postulates

ASA (Angle - Side - Angle) requires two angles and the included side to be equal. AAS (Angle - Angle - Side) requires two angles and a non - included side to be equal. SAS (Side - Angle - Side) requires two sides and the included angle to be equal. HL (Hypotenuse - Leg) is for right - angled triangles where hypotenuse and one leg are equal.

Step3: Apply the postulate

We have two angles ($\angle A=\angle C$ and $\angle ABD=\angle CBD$) and a non - included side ($BD$). So, the congruence postulate is AAS.

Answer:

b. AAS