Question

question 1 of 10
based on the information marked in the diagram, \\( \triangle a b c \\) and \\( \triangle d e f \\) must be congruent.

a. true
b. false

Explanation:

Step1: Recall the congruence criteria for right - angled triangles

For right - angled triangles (\(\triangle ABC\) with \(\angle C = 90^{\circ}\) and \(\triangle DEF\) with \(\angle F=90^{\circ}\)), we can use the Hypotenuse - Leg (HL) congruence criterion. But we only know that one leg (\(AC = DF\)) is equal. We don't know about the hypotenuses (\(AB\) and \(DE\)) or the other legs (\(BC\) and \(EF\)).

Step2: Analyze the given information

Just having one pair of legs equal is not sufficient to prove congruence. For example, if \(AC = DF\), but \(BC
eq EF\) and \(AB
eq DE\), the triangles are not congruent.

Answer:

B. False