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

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

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Step-by-step video solution

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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!

Step-by-step written solution

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1

Understand the problem

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

2

Step-by-step solution

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:

ABDE=408=5 \frac{AB}{DE}=\frac{40}{8}=5

ACDF=459=5 \frac{AC}{DF}=\frac{45}{9}=5

3

Final Answer

AB=40 DF=9

AC=45 DE=8

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