Question

Please answer and show all work (15 points!)

Answer 1

Question 1:

In ΔSTU and ΔDEU,

$\frac{SU}{DU} = \frac{39}{16}$ ≠ $\frac{40}{16} = \frac{TU}{EU}$

∠SUT = ∠DUE  [ Opposite angles ]

Thus, ΔSTU and ΔDEU are NOT similar. as the ratio of the length of the sides is not a constant.

Question 2:

In ΔABC and ΔHGF,

$\frac{AB}{HG} = \frac{72}{12} = 6$

$\frac{AC}{HF} = \frac{84}{14} = 6$

$\frac{BC}{GF} = \frac{48}{8} = 6$

Thus, $\frac{AB}{HG}= \frac{AC}{HF} = \frac{BC}{GF} = 6$

Hence, ΔABC and ΔHGF are similar by SSS similarity criterion.