Question

Prove that DJKL~ DJMN using SAS Similarity Theorem. Plot the points J (1,1), K(2,3), L(4,1) and J (1,1), M(3,5), N(7,1). Draw DJKL and DJMN.

Answer 1

Answer and Step-by-step explanation: The triangles are plotted and shown in the attachment.

SAS Similarity Theorem is by definition: if two sides in one triangle are proportional to two sides of another triangle and the angles formed by those sides in each triangle is congruent, the triangles are similar.

For the triangles on the grid, we know that ΔJKL and ΔJMN have a congruent angle in J as shown in the image. To prove they are similar, we find the slope of sides KL and MN:

Slope of KL:

slope = $\frac{y_{K} - y_{L} }{x_{K} - x_{L} }$

slope = $\frac{3-1}{2-4}$

slope = -1

Slope of MN:

slope = $\frac{y_{N} - y_{M} }{x_{N} - x_{M} }$

slope = $\frac{1-5}{7-3}$

slope = -1

Since the slopes of KL and MN are the same and the angle is congruent, we can conclude that ΔJKL~ΔJMN.