Question

If ∆PQR ≅ ∆XYZ, Which of the following is true?

Answer 1

Answer:

this two angles are congruent to each other

Answer 2

Correct question:

If  ΔPQR ≅ ΔXYZ, then which of the following is true?

(a)angle P is congruent to angle Y

(b)angle Q is congruent to angle Z

(c)angle R is congruent to angle X

(d)angle R is congruent to angle Z

If ∆PQR ≅ ∆XYZ, then (d)angle R is congruent to angle Z is true.

Step-by-step explanation:

Given:

∆PQR ≅ ∆XYZ

To find:

Correct option in relation to given

Solution:

∆PQR ≅ ∆XYZ,

According to the congruent triangle theorem, the corresponding angles and corresponding sides of the congruent triangles will be congruent.

The corresponding angles of the given two triangles will be  ∠P and ∠X, ∠Q and ∠Y, ∠R and ∠Z

∴ ∠P≅∠X.....(corresponding angles of congruent triangles are congruent)

  ∠Q≅∠Y......(corresponding angles of congruent triangles are congruent)

  ∠R≅∠Z....(corresponding angles of congruent triangles are congruent)(1)

• (a) angle P is congruent to angle Y cannot be true as those are not corresponding angles.
• (b)angle Q is congruent to angle Z cannot be true either as the corresponding angle of Q is the angle Y
• (c)angle R is congruent to angle X is not true because they are not corresponding angles

Thus from (1) we get that (d)angle R is congruent to angle Z is true