Question

question 10 of 10
based on the information marked in the diagram, △xyz and △rst must be congruent.
a. true
b. false

Explanation:

Step1: Recall congruent triangle criteria

For right - angled triangles, we have criteria like HL (Hypotenuse - Leg), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), SAS (Side - Angle - Side), SSS (Side - Side - Side). Here, we have two right - angled triangles (\(\angle Z=\angle T = 90^{\circ}\)), one pair of equal angles (\(\angle X=\angle R\)) and one pair of equal sides (the marked sides \(YZ = ST\)).

Step2: Apply AAS criterion

In \(\triangle XYZ\) and \(\triangle RST\), \(\angle Z=\angle T\), \(\angle X=\angle R\), and \(YZ = ST\). By the AAS (Angle - Angle - Side) congruence criterion for triangles (if two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, then the two triangles are congruent), \(\triangle XYZ\cong\triangle RST\).

Answer:

A. True