Question

Name:Date:Similar Triangles with shared anglesVerify that the triangles are similar and solve for the missing side length. Be sure to draw andlabel two separate triangles.#1

Answer 1

#1

I will draw the figure to see it and work on it

From the figure

Since CD // DE, then

From these conditions

Triangle ABC is similar to triangle AED

As a result of similarity, their corresponding sides are proportional

$\frac{AB}{AE}=\frac{AC}{AD}$

Since AB = 7, AE = 7 + x

Since AC = 5, AD = 5 + 3 = 8

Then

$\frac{7}{(7+x)}=\frac{5}{8}$

By using cross multiplication

$5(7+x)=7(8)$

Simplify it

$\begin{gathered} 5(7)+5(x)=56 \\ 35+5x=56 \end{gathered}$

Subtract 35 from both sides

$\begin{gathered} 35-35+5x=56-35 \\ 5x=21 \end{gathered}$

Divide both sides by 5

$\begin{gathered} \frac{5x}{5}=\frac{21}{5} \\ x=4.2 \end{gathered}$

Then the missing part x is 4.2