Question

question 2 of 10
based on the information marked in the diagram, (\triangle xyz) and (\triangle rst) must be congruent.
a. true
b. false

Explanation:

Step1: Recall congruent triangle criteria

For right - angled triangles, the Hypotenuse - Leg (HL) congruence criterion is used. But here, we only know one pair of angles (the right angles and one acute angle) and one pair of legs (the marked equal sides).

Step2: Check for sufficient congruence information

The given information does not satisfy any of the congruence criteria (SSS - Side - Side - Side, SAS - Side - Angle - Side, ASA - Angle - Side - Angle, AAS - Angle - Angle - Side, HL - Hypotenuse - Leg for right - angled triangles). We don't know if the other sides (hypotenuse or the other leg) are equal.

Answer:

B. False