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

`(AB)/(AE)=(AC)/(AD)`

Since AB = 7, AE = 7 + x

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

Then

`(7)/((7+x))=(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} (5x)/(5)=(21)/(5) \\ x=4.2 \end{gathered}`

Then the missing part x is 4.2