Question

Identify the pair of similar triangles in the figure. Angle ABC Angle DEF Angle GHK

Answer 1

• ∆ABC
• ∆DEF

Explanation:

You can use Triangle angle sum theorem which states that the sum of the interior angles must be 180°.

This means that 180 subtracted from the two other angles can be used to find the unknown if there isn't two angles in common already. Then use the AA similarity theorem to prove it.

We can check ABC first, so 180 - (57 + 38) = 85.

DEF has 85°, 57°, ?

ABC has 57°, 38°, 85°

Once again, we can prove they are truly similar since all the angles will match up too:

With DEF → ? = 180 - (85 + 57) = 38

DEF has 85°, 57°, 38°

ABC has 57°, 38°, 85°