Question

are these triangles congruent? if so, state the rule which you used to determine congruence. hl asa ssa sas

Explanation:

Step1: Recall congruence rules

• HL (Hypotenuse - Leg): For right - angled triangles, if the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): 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.
• SSA (Side - Side - Angle): Not a valid congruence rule in general (except for right - angled triangles in the form of HL).
• SAS (Side - Angle - Side): 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

• Both \(\triangle ABC\) and \(\triangle XYZ\) are right - angled triangles (\(\angle A = 90^{\circ}\) and \(\angle X=90^{\circ}\)).
• Let's assume the hypotenuse \(CB = ZY\) (marked with two lines) and one leg \(AB = XY\) (marked with one line).

Since we have two right - angled triangles with the hypotenuse and one leg equal, we use the HL (Hypotenuse - Leg) congruence rule.

Answer:

HL