Question

1. determine which method if any can prove the triangles are congruent.

sss
sas
asa
aas
hl
not possible

1. determine which method if any can prove the triangles are congruent.

there is than one, check all that apply

Explanation:

Step1: Recall congruence criteria

For triangle congruence, we have SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze problem 8

In problem 8, we have two sides and the included angle marked.
SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

Step3: Analyze problem 9

In problem 9, we have a rectangle. In a rectangle, opposite sides are equal and all angles are right angles.

• For SSS: The diagonal is common to both triangles. The opposite sides of the rectangle are equal. So, three pairs of sides are equal (two pairs of opposite sides of the rectangle and the common diagonal).
• For HL: Since the triangles are right - triangles (angles of the rectangle are right angles), and the hypotenuse (diagonal) is common and the legs (sides of the rectangle) are equal.

Answer:

1. SAS
2. SSS, HL