Question

10 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

In the given triangles, we are only given information about the sides (marked with tick marks). There is no information about the angles.

Step3: Check the congruence theorems

• For SAS, we need an angle between two sides.
• For ASA and AAS, we need angles.
• For HL, we need to know that the triangles are right - angled.
• Since we only have information about the sides and no information about the angles (and we don't know if they are right - angled), we cannot use SAS, ASA, AAS, or HL. Also, we don't have information that all three sides are equal (SSS requires all three sides of one triangle equal to all three sides of another triangle).

Answer:

Cannot be proven congruent