Question

Short Answer

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Are the two triangles similar? How do you know?

Answer 1

Yes, the triangles are similar

Explanation:

In order for two triangles to be similar, at least two corresponding angles must be congruent.

We know DCE and GFH are congruent, because they are both 60°, so that's one angle down, now we need one more.

We can either choose to see if CDE and FGH are the same, or CED and FHG. I'll choose CDE and FGH.

We know CDE is 53°, so we need to find FGH to see if it's also 53°.

The sum of the interior angles of a triangle are 180°, so we can find FGH by doing 180-60-67=53°, so CDE and FGH are congruent.

Knowing DCE and GFH are congruent, and CDE and FGH are congruent, we can say that these triangles are similar.

Answer 2

Yes, they are similar in terms of the size of their angles.

Explanation:

The angles of a triangle always add up to 180°, so

Triangle CDE's missing angle: 180 - (60 + 53) = 67

Triangle FGH's missing angle: 180 - (67 + 60) = 53