Question

given the triangles below with sides and angles as marked.
select the postulate or theorem that proves these triangles are congruent.
hypotenuse leg congruence theorem
angle angle side congruence theorem
side side side congruence postulate
these triangles are not congruent.
angle side angle congruence postulate
side angle side congruence postulate

Explanation:

Step1: Recall congruence theorems

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

Step2: Analyze the given triangles

The given triangles are right - angled (right angles are marked). We know that one leg (marked as equal) and the hypotenuse (the common side opposite the right angle) are equal.

Answer:

Hypotenuse Leg Congruence Theorem