Question

In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement ∠Q ≅ ___

Answer 1

Answer:  Choice A.  $\angle T$

Explanation:

Notice how letters Q and T are in the middle of the sequences of PQR and STR respectively. This means the angles correspond.

Because the triangles are congruent, this means the corresponding pieces are congruent. Therefore, angle Q and angle T are the same measure.

As you can see, the order matters when it comes to forming congruence statements. Something like $\triangle PQR \cong \triangle STR$ is slightly different from $\triangle PQR \cong \triangle SRT$

Answer 2

Congruent triangles have all corresponding measurements like angles and side lengths congruent. The completed statement would be ∠Q ≅ ∠T (Option A: ∠T)

What are congruent triangles?

Suppose it is given that two triangles ΔABC  ≅ ΔDEF

Then that means ΔABC  and  ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC  ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

• $\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D$ (small m shows we're taking about measurement) (both the statements are equivalent)
• $\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E$
• $\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F$
• $\rm |AB| = |DE| \: \: or \: \: AB \cong DE$
• $\rm |AC| = |DF| \: \: or \: \: AC \cong DF$
• $\rm |BC| = |EF| \: \: or \: \: BC \cong EF$

(|AB| denotes length of line segment AB, and so on for others).

For this case, we have:  ΔPQR ≅ ΔSTR

Thus, we have:

$\angle Q = \angle T$

Thus, the completed statement would be ∠Q ≅ ∠T. (Option A: ∠T)

Learn more about congruent triangles here:

https://brainly.com/question/16921692