Question

May I please get help with this problem? It’s really confusing and I’ve tried times

Answer 1

Part A:

Aligning the corresponding of each of the triangles we have

∠D corresponds to ∠T (red angle in both triangles)

∠E corresponds to ∠S (blue angle in both triangles)

∠F corresponds to ∠R (black angle in both triangles)

Therefore, the congruence statements are as follows

$\begin{gathered} \angle D\cong\angle T \\ \angle E\cong\angle S \\ \angle F\cong\angle R \end{gathered}$

Part B:

Given the dimensions of both of the triangle we have

ΔDEF:

DE = 16, EF = 18, DF = 10

ΔTSR:

TS = 24, SR = 27, TR = 15

Substitute the following dimensions to the ratios and simplify

$\begin{gathered} \frac{TS}{DE}=\frac{24}{16}=\frac{3}{2}\text{ (simplified)} \\ \\ \frac{SR}{EF}=\frac{27}{18}=\frac{3}{2}\text{ (simplified)} \\ \\ \frac{TR}{DF}=\frac{15}{10}=\frac{3}{2}\text{ (simplified)} \end{gathered}$

Part C:

Since the corresponding angles of ΔDEF, and ΔTSR are congruent, and the ratio of the corresponding sides are all equal, then we can conclude that

ΔDEF and ΔTSR are similar