Question

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

Explanation:

Step1: Identify triangle properties

Both $\triangle FGH$ and $\triangle JKL$ are right triangles ($\angle F = \angle J = 90^\circ$). We have:

• $FG \cong JK$ (single tick mark)
• $FH \cong JL$ (double tick mark)

Step2: Apply congruence rule

For right triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another triangle, the triangles are congruent (HL Congruence Theorem). Here, the hypotenuses are $GH$ and $KL$, and we have a pair of congruent legs ($FG \cong JK$) and congruent other sides ($FH \cong JL$, which are the other legs of the right triangles, satisfying HL).

Step3: Verify congruence

Since we have two pairs of corresponding congruent sides including the right angle, the triangles must be congruent.

Answer:

A. True