If ΔPRQ

Question

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

SSS
SSS

ASA
ASA

SAS
SAS

AA

Answer 1

To determine if the triangles ΔPRQ and ΔFGH are similar, we need to analyze the angles given.

In ΔPRQ:

• ∠P = 30°
• ∠R = 127°

To find ∠Q, we can use the fact that the sum of the angles in a triangle is 180°:

∠Q = 180° - (∠P + ∠R) ∠Q = 180° - (30° + 127°) = 180° - 157° = 23°

In ΔFGH:

• ∠H = 30°
• ∠G = 23°

To find ∠F, we also use the same principle:

∠F = 180° - (∠H + ∠G) ∠F = 180° - (30° + 23°) = 180° - 53° = 127°

Now we have the angles:

• In ΔPRQ: ∠P = 30°, ∠R = 127°, ∠Q = 23°
• In ΔFGH: ∠H = 30°, ∠G = 23°, ∠F = 127°

Comparing the angles:

• ∠P = ∠H = 30°
• ∠R = ∠F = 127°
• ∠Q = ∠G = 23°

Since two triangles have two pairs of corresponding angles equal, they are similar by the AA (Angle-Angle) criterion.

Therefore, the correct answer is AA.