Proving Triangle Similarity Examples

If all three sides of ∆MON are 3 units long, is it true that ∆MON ~ ∆KEY?

∆MON is equilateral, since we're given that all three sides are congruent. ∆KEY is also equilateral, because its three angles are congruent. (Remember that equiangular triangles are always equilateral!) Since both triangles are equilateral, we know that they're similar, because all equilateral triangles are similar to each other.

Prove that these triangles are similar.

We know from the drawing that there are two sets of parallel lines that both intersect the same transversal, which makes for plenty of corresponding angles. Fortunately, there's a theorem for that (Corresponding Angles Theorem).

Prove that ∆WTC ~ ∆WIH using the Side-Angle-Side Postulate.

It must have been Glinda that wrote this one, since she already gave us the final statement and reason of our proof. That also gives us an idea of where we need to start, since knowing the end means we know what we need to prove: that there are two sets of proportional sides with a congruent angle in between.

Statement	Reason
1. ∠TWC ≅ ∠IWH	Reflexive Property
2. IH || TC	Given
3.	Corollary of Triangle Midsegment Theorem
4. ∆WTC ~ ∆WIH	Side-Angle-Side Postulate

Prove that these triangles are similar.

More parallel lines crossing a transversal, this time creating angles on the inside (interior) of the polygon. Follow the yellow brick…