Question

If ΔPRQ
has ∠P=30
and ∠R=127
and ΔFGH
has ∠H=30
and ∠G=23
, what criterion has been met to prove the triangles similar?(1 point)
Responses

AA
AA

ASA
ASA

SSS
SSS

SAS

Answer 1

To determine if triangles ΔPRQ and ΔFGH are similar, we can use the angle-angle (AA) similarity criterion.

For triangle ΔPRQ:
- ∠P = 30°
- ∠R = 127°

To find ∠Q, we can sum the angles in a triangle which equal 180°:
∠Q = 180° - ∠P - ∠R = 180° - 30° - 127° = 23°.

For triangle ΔFGH:
- ∠H = 30°
- ∠G = 23°

We can find ∠F as follows:
∠F = 180° - ∠H - ∠G = 180° - 30° - 23° = 127°.

Now we can see the angles of the triangles:
- Triangle ΔPRQ has angles: 30°, 127°, 23°.
- Triangle ΔFGH has angles: 30°, 23°, 127°.

Since both triangles have two pairs of equal angles (30° and 23°), we can apply the AA criterion (Angle-Angle) for similarity.

**Answer: AA**