Question

Lorie correctly determines that for the triangles below, the statement pg and the statement both describe the relationship between the two triangles.
Which best describes why both similarity statements are correct?
Each triangle has two congruent angles: and m.
Each triangle has two similar angles: and .
The triangles each have two given angle measures and one unknown angle measure.
All statements, regardless of the order of the vertices, define the same triangles

Answer 1

Answer:

The correct option is 1.

Step-by-step explanation:

Two triangles are called similar if all the corresponding angles are congruent or all corresponding sides are in same proportion.

In triangle MNO and triangle RTS.

$\angle M\cong\angle R=54.4^{\circ}$          (Given)

$\angle N\cong\angle T=71.2^{\circ}$            (Given)

According to the angle sum property, the sum of all interior angles of a triangle is 180 degree. Since two corresponding angles are congruent, therefore third angle is also congruent.

$\angle O\cong\angle S=54.4^{\circ}$

Since all corresponding angles are congruent, therefore the triangles MNO and RTS similar.

The triangle are congruent by AA rule of similarity. Each triangle has two congruent angles, therefore both triangles are similar. Option 1 is correct.

Answer 2

Answer:

A

Step-by-step explanation: