Question

the triangles can be proven similar by applying the similarity criteria for

Explanation:

⚡ Using what you learned: similarity criteria for triangles (aa, sss, sas)

Step 1: Find the missing angle in triangle GHI

The sum of angles in any triangle is always \( 180^\circ \).

$$ m\angle G + m\angle H + m\angle I = 180^\circ $$

$$ m\angle G + 86^\circ + 51^\circ = 180^\circ $$

$$ m\angle G + 137^\circ = 180^\circ $$

$$ m\angle G = 43^\circ $$

Step 2: Compare the angles of both triangles

Now we compare the interior angles of \(\triangle GHI\) and \(\triangle CAB\):

• \( m\angle G = 43^\circ \) and \( m\angle A = 43^\circ \) (First pair of congruent angles: \(\angle G \cong \angle A\))
• \( m\angle H = 86^\circ \) and \( m\angle B = 86^\circ \) (Second pair of congruent angles: \(\angle H \cong \angle B\))

Since two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Answer:

AA