Question

are these triangles congruent? if so, state the rule which you used to determine congruence. sas asa not congruent sss

Explanation:

Step1: Recall congruence rules

• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides of another triangle.

Step2: Analyze the given triangles

• From the figure, we can see that two sides of one triangle are equal to two sides of the other triangle (marked with double and single hash - marks respectively).
• The vertical angles (opposite angles formed by the intersection of two lines) are equal. The vertical angles are the included angles for the two pairs of equal sides.

Step3: Apply the congruence rule

• Since we have two sides and the included angle (vertical angles are equal) of one triangle equal to two sides and the included angle of the other triangle, we use the SAS (Side - Angle - Side) congruence rule.

Answer:

SAS