Question

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

Explanation:

Step1: Recall congruence postulates and theorems

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

Step2: Analyze the given triangles

Both triangles are right - angled (one right angle). They have two pairs of equal non - right angles. In the AAS theorem, when two angles of one triangle are equal to two angles of another triangle, the third angle is also equal (since the sum of angles in a triangle is \(180^{\circ}\)). And we can consider the non - included sides (the sides opposite to one of the non - right angles). So, by the Angle Angle Side (AAS) Congruence Theorem, the two triangles are congruent.

Answer:

Angle Angle Side Congruence Theorem