Question

based on the information marked in the diagram, $\triangle abc$ and $\triangle def$ must be congruent.
a. true
b. false

Explanation:

Step1: Identify triangle properties

Both $\triangle ABC$ and $\triangle DEF$ are right triangles, with $\angle A = \angle D = 90^\circ$. We have $\overline{AC} = \overline{DF}$ (marked with double hash marks) and $\overline{BC} = \overline{EF}$ (marked with single hash marks).

Step2: Apply congruence rule

For right triangles, if the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle, the triangles are congruent (HL Congruence Theorem). Here, $\overline{BC},\overline{EF}$ are hypotenuses, $\overline{AC},\overline{DF}$ are legs.

Answer:

A. True