Question

12 multiple choice 1 point the following triangles can be proven congruent by which theorem, if any? sas sss asa aas hl cannot be proven congruent clear my selection

Explanation:

Step1: Recall Congruence Theorems

• 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.
• SSS (Side - Side - Side): All three sides of one triangle are equal to all three sides 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.
• AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle.
• HL (Hypotenuse - Leg): For right - angled triangles, the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled 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 triple lines respectively), and the included angle (the vertical angles are equal) is also equal.

Answer:

SAS