Similar Figures in the Coordinate Plane Quick Check 3 of 53 of 5 Items 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 ASA ASA AA AA SAS SAS SSS SSS Skip to navigation page 21 of 21 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the similarity criterion that has been met for triangles ΔPRQ and ΔFGH, we can analyze the given angles.

1. For triangle ΔPRQ:

   • ∠P = 30°
   • ∠R = 127°
   • Since the sum of angles in a triangle is 180°, we can find ∠Q:
     • ∠Q = 180° - ∠P - ∠R = 180° - 30° - 127° = 23°.

2. For triangle ΔFGH:

   • ∠H = 30°
   • ∠G = 23°.
   • Similar to above, we can find ∠F:
     • ∠F = 180° - ∠H - ∠G = 180° - 30° - 23° = 127°.

Now we can compare the angles of both triangles:

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

We can see that:

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

Since all corresponding angles are equal, we can conclude that the triangles are similar by the AA (Angle-Angle) similarity criterion.

So the correct response is AA.