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

Question

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

00:07 Let's find the side lengths so that the triangles are similar.

00:11 First, we need to find the ratio of the sides.

00:15 Next, substitute the correct values based on the given information.

00:20 Now, find the ratio between the first pair of sides and the second pair.

00:25 Again, use the given data to substitute the right values.

00:30 If the side ratios match, then the triangles are similar.

00:34 And that's how we solve this problem!

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