Question

Q

R
In the
diagram
below, right
triangle PQR is
transformed by a
sequence of rigid
motions that maps it
onto right triangle NML.
P M
N
Write a set of three congruency
statements that would show ASA
congruency for these triangles.

Answer 1

The three congruency statements that can be used to show that both triangles are congruent by ASA congruence theorem are:

∠Q ≅ ∠M; QP ≅ MN; QR ≅ ML.

What is the ASA Congruency Theorem?

The ASA (Angle-Side-Angle) Congruency Theorem states that if two triangles have two angles and the included side of one triangle congruent to the corresponding angles and side of another triangle, then the triangles are congruent.

Since right triangle PQR is mapped onto right triangle NML, therefore, the following congruency statements can be deduced to show ASA congruency:

∠Q ≅ ∠M [included angle]

QP ≅ MN and QR ≅ ML.