Question

1. name the postulate or theorem you can use to prove the triangles congruent. asa postulate sas postulate hl theorem aas theorem

Explanation:

Step1: Recall triangle congruence criteria

• 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.
• 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.
• HL (Hypotenuse - Leg) 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 triangles are congruent.
• 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.

Step2: Analyze the given right - angled triangles

• The given triangles are right - angled (right angle is one of the angles).
• We can observe that the hypotenuse (the longest side, marked with one tick) and one leg (marked with two ticks) of each right - angled triangle are equal.

Answer:

HL Theorem