Question

on #7: Explain if the triangles are similar using AA-, SSS-, or SAS- If they are similar, how do you know they are similar? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)

Answer 1

EXPLANATION

The triangles have the following included and congruent angles:

∠XLY ≅ ∠GLB

Now, by SAS Postulate we shall prove that the two sides are similar.

Considering the relationship between sides:

XL/GL ≠ YL / VL

30/(9+30)≠ 27/(7+27)

Adding terms:

30/39 ≠27/ 34

Simplifying:

10/13 ≠ 27/34

The triangles are not similar because the relationship between the sides is not the same, and by Side-Angle-Side Congruence Postulate: "If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent".