Question

Explain if the triangles are similar using SAS-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)

Answer 1

We have two triangles GBL and XYL.

From the picture we notice that the GL=39 and BL=34. We also notice that XL=30 and YL=27.

The SAS theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

This means that we need that:

`(GL)/(XL)=(BL)/(YL)`

and that the angle between them is the same.

It is clear that the angle L is the same for both triangles, hence we only need to proof tha the sides are congruent, but in this case:

`(39)/(30)\\e(34)/(27)`

since the sides are not proportional, we conclude that triangles are not congruent.