Question

Triangle LMO with angle L 70 degrees and angle M 52 degrees; triangle PQR with angle Q 58 degrees and angle R 52 degrees

Determine if the two triangles are similar. If so, write the similarity statement. Enter the answer.

Answer 1

To determine if triangles LMO and PQR are similar, we can use the criteria that if two triangles have corresponding angles that are equal, then the triangles are similar.

For triangle LMO:
- Angle L = 70 degrees
- Angle M = 52 degrees
- Angle O can be found by using the fact that the sum of angles in a triangle is 180 degrees:
\[
Angle O = 180 - (70 + 52) = 180 - 122 = 58 \text{ degrees}
\]

So, the angles in triangle LMO are:
- Angle L = 70 degrees
- Angle M = 52 degrees
- Angle O = 58 degrees

For triangle PQR:
- Angle Q = 58 degrees
- Angle R = 52 degrees
- Angle P can be found similarly:
\[
Angle P = 180 - (58 + 52) = 180 - 110 = 70 \text{ degrees}
\]

So, the angles in triangle PQR are:
- Angle P = 70 degrees
- Angle Q = 58 degrees
- Angle R = 52 degrees

Now we can compare the angles of the two triangles:
- Triangle LMO: 70°, 52°, 58°
- Triangle PQR: 70°, 58°, 52°

Since the corresponding angles are equal (Angle L = Angle P, Angle M = Angle R, Angle O = Angle Q), we conclude that the triangles are similar.

The similarity statement can be written as:
\[
\triangle LMO \sim \triangle PQR
\]