Question

determine if the two triangles are necessarily congruent. if so, fill in a flowchart proof to prove that they are. the triangles are (\triangle def) and (\triangle srp). for each of the first three boxes, choose a statement format from the dropdown menu. you will then be able to change the letters to match the diagram for this problem. de (cong) sr reason: (angle dcongangle s) reason: (angle fcongangle p) reason:

Explanation:

Step1: Identify congruence criteria

In right - angled triangles $\triangle DEF$ and $\triangle RPS$, we have right angles $\angle F=\angle P = 90^{\circ}$. Also, we are given that $DE = SR$ (hypotenuse) and a non - hypotenuse side is equal (the single - marked sides). By the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles, the two triangles are congruent.

Step2: State congruent parts

For congruent triangles $\triangle DEF\cong\triangle RPS$, corresponding parts are congruent. So, $\overline{DE}\cong\overline{SR}$ because they are corresponding hypotenuses of congruent right - angled triangles. $\angle D\cong\angle S$ as they are corresponding angles in congruent triangles. $\angle F\cong\angle P$ because both are right angles (by definition of right - angled triangles).

Answer:

$\overline{DE}\cong\overline{SR}$ (Hypotenuse - Leg congruence of right - angled triangles), $\angle D\cong\angle S$ (Corresponding parts of congruent triangles), $\angle F\cong\angle P$ (Both are right angles)