Question

similar figures in the coordinate plane quick check
if ( \triangle prq ) has ( angle p = 30 ) and ( angle r = 127 ) and ( \triangle fgh ) has ( angle h = 30 ) and ( angle g = 23 ), what criterion has been met to prove the triangles similar? (1 point)
sss
sas
asa
aa

Explanation:

Step1: Find the third angle of \(\triangle PRQ\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle PRQ\), if \(\angle P = 30^{\circ}\) and \(\angle R=127^{\circ}\), then \(\angle Q=180-(30 + 127)=23^{\circ}\)

Step2: Match the angles

In \(\triangle PRQ\), \(\angle P = 30^{\circ}\), \(\angle Q = 23^{\circ}\). In \(\triangle FGH\), \(\angle H=30^{\circ}\), \(\angle G = 23^{\circ}\). Two pairs of corresponding angles are equal.

Answer:

AA (Angle - Angle) criterion is met. So the answer is the option labeled "AA".