Question

4.4 assignment
state the third congruence that must be given to prove △jrm ≅ △dfb using the indicated postulate.
given: overline{jm} ≅ overline{db}, ∠j is a right angle, and ∠j ≅ ∠d
use the hl congruence theorem.

Explanation:

Step1: Recall HL Congruence Theorem

HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.

Step2: Identify legs and hypotenuses

In right - triangle \( \triangle JRM\) and \( \triangle DFB\), we are given that \( \overline{JM}\cong\overline{DB}\) (a leg). We know that \( \angle J\) and \( \angle D\) are right angles. For the HL theorem, we need to show that the hypotenuses are congruent.
The hypotenuse of \( \triangle JRM\) is \( \overline{RM}\) and the hypotenuse of \( \triangle DFB\) is \( \overline{FB}\).

Answer:

\(\overline{RM}\cong\overline{FB}\)