Question

determine which triangle congruence theorem explains how the triangles are congruent. side-side-side congruence theorem angle-side-angle congruence theorem side-angle-side congruence theorem hypotenuse-leg congruence theorem

Explanation:

Step1: Recall triangle congruence theorems

• Side - Side - Side (SSS) Congruence Theorem: If three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.
• Angle - Side - Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
• Side - Angle - Side (SAS) Congruence Theorem: 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.
• Hypotenuse - Leg (HL) Congruence Theorem: For right - angled triangles, if the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, then the two right - angled triangles are congruent.

Step2: Analyze the given triangles

The markings on the triangles show that all three sides of one triangle are equal to all three sides of the other triangle.

Answer:

Side - Side - Side Congruence Theorem