To determine which criterion shows that the triangles ΔPRQ and ΔFGH are similar, we need to check their angle measures.
For triangle ΔPRQ, the angles are:
- ∠P = 30°
- ∠R = 127°
To find the third angle (∠Q), we use the fact that the sum of the angles in a triangle is 180°:
\[ ∠Q = 180° - ∠P - ∠R = 180° - 30° - 127° = 23° \]
So, the angles in triangle ΔPRQ are:
- ∠P = 30°
- ∠R = 127°
- ∠Q = 23°
For triangle ΔFGH, the angles are:
- ∠H = 30°
- ∠G = 23°
To find the third angle (∠F), we again use the angle sum property:
\[ ∠F = 180° - ∠H - ∠G = 180° - 30° - 23° = 127° \]
So, the angles in triangle ΔFGH are:
- ∠H = 30°
- ∠G = 23°
- ∠F = 127°
Now we have the angle measures for both triangles:
- Triangle ΔPRQ: 30°, 127°, 23°
- Triangle ΔFGH: 30°, 23°, 127°
We see that both triangles have two angles that are equal:
- ∠P = ∠H = 30°
- ∠G = ∠Q = 23°
Both triangles satisfy the AA (Angle-Angle) criterion for similarity since two angles in one triangle are equal to two angles in the other triangle.
Therefore, the correct response is:
AA
6 answers