Question

1. which of the following sets of triangles can be proved congruent using the aas theorem?
2. in the figure ij = kj and hj = jl. which of the following statements about congruence is true?

a. $\triangle hij \cong \triangle alk)$ by asa
b. $\triangle hij \cong \triangle akl)$ by sss
c. $\triangle hij \cong \triangle akl)$ by sas
d. $\triangle hij \cong \triangle alk)$ by sas

1. refer to the figure to complete the congruence statement, $\triangle abc \cong$ ____ and $\triangle abe \cong$ ____

Explanation:

Step1: Recall AAS Theorem

AAS (Angle - Angle - Side) Theorem 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, then the two triangles are congruent.

Step2: Analyze each option

• For option a: Check the marked angles and sides. The marked angles and sides do not seem to satisfy AAS (two angles and a non - included side).
• For option b: The marked angles and sides do not match the AAS criteria.
• For option c: Let's assume the triangles in option c. If we can identify two angles and a non - included side that are congruent. Looking at the markings, we can see that two angles and a non - included side are congruent, which satisfies the AAS theorem.
• For option d: The markings do not correspond to the AAS congruence criteria.

Answer:

c (assuming the option c is the set of triangles with markings that satisfy AAS, based on the visual analysis of angle and side markings)