Similar Triangles Construction: Finding Lengths with ∢A=∢D

Question

Given two triangles. Choose appropriate lengths to obtain similar triangles if given $∢A=∢D$

00:00 Find the side lengths so that the triangles are similar

00:03 Find the ratio of sides

00:07 Substitute appropriate values according to the given data

00:13 Find the ratio between the sides and the second sides

00:17 Substitute appropriate values according to the given data

00:21 The side ratios are equal, therefore the triangles are similar

00:24 And this is the solution to the question

The correct answer is D. Since angle A is equal to angle D, then BAC is similar to FDE

Therefore, we calculate according to the data from answer D as follows:

$\frac{AB}{DE}=\frac{40}{8}=5$

$\frac{AC}{DF}=\frac{45}{9}=5$

AB=40 DF=9

AC=45 DE=8