Question

Lorie correctly determines that for the triangles below, the statement Triangle N M O is similar to triangle T S R and the statement Triangle N M O is similar to triangle T R S both describe the relationship between the two triangles. Triangle M N O. Angle M is 54.4 degrees and angle N is 71.2 degrees. Triangle R S T. Angle R is 54.4 degrees and angle T is 71.2 degrees. Which best describes why both similarity statements are correct? Each triangle has two congruent angles: Angle M is congruent to angle O and Angle R is congruent to angle S. Each triangle has two similar angles: Angle M is similar to angle O and Angle R is similar to angle S. 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

A

Explanation:

Just did the test.

Answer 2

(A)Each triangle has two congruent angles: Angle M is congruent to angle O and Angle R is congruent to angle S.

Explanation:

In Triangle MNO

`\angle M = 54.4$ degrees, \angle N = 71.2$ degrees\\\angle M+\angle N+\angle O=180^\circ\\54.4^\circ+71.2^\circ+\angle O=180^\circ\\\angle O=180^\circ-(54.4^\circ+71.2^\circ)=54.4^\circ`

In Triangle RST

`\angle R = 54.4$ degrees, \angle T = 71.2$ degrees\\\angle R+\angle T+\angle S=180^\circ\\54.4^\circ+71.2^\circ+\angle S=180^\circ\\\angle S=180^\circ-(54.4^\circ+71.2^\circ)=54.4^\circ`

Therefore:

Triangle NMO is congruent to triangle TSR; and

Triangle NMO is congruent to triangle TRS

This is because

`\angle M \cong \angle O =54.4^\circ; and\\ \angle R \cong \angle S =54.4^\circ .`

The correct option is A.