Question

7 multiple choice 10 points
determine if each pair of triangles is congruent. if so, write the postulate or theorem.
image of a quadrilateral with triangles abc and adc
options:
sas
triangles are not congruent.
sss
aas
asa
hl

8 multiple choice 10 points
determine if each pair of triangles is congruent. if so, write the postulate or theorem.
image of triangles abc and dec
options:
asa
hl
aas
the triangles are not congruent.

Explanation:

Question 7

Step1: Identify Common Side

Triangles \( \triangle ABC \) and \( \triangle ADC \) share side \( AC \), so \( AC = AC \) (reflexive property).

Step2: Identify Marked Sides and Angles

We see \( AB = AD \) (marked with one tick) and \( \angle BAC = \angle DAC \) (marked with the angle symbol).

Step3: Apply SAS Postulate

SAS (Side - Angle - Side) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. Here, \( AB = AD \), \( \angle BAC=\angle DAC \), and \( AC = AC \), so by SAS, the triangles are congruent.

Step1: Analyze Given Information

We have triangles \( \triangle ABC \) and \( \triangle DEC \). We know that \( \angle ACB=\angle DCE \) (vertical angles are congruent), but we need to check other corresponding parts. From the diagram, we don't have enough information (like two sides and included angle, or two angles and included side, etc.) to prove congruence. So the triangles are not congruent.

Answer:

A. SAS

Question 8