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 two triangles ΔPRQ and ΔFGH are similar based on the given angle measures, we can use the Angle-Angle (AA) similarity criterion.

For ΔPRQ:

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

For ΔFGH:

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

Now we can see that:

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

Since the two triangles have two pairs of corresponding angles equal, we can conclude the triangles are similar by the AA criterion.

The correct response would be:

AA