Solving Similar Triangles

Question 1 of 5

The following two triangles are similar.

Solve for the missing sides

x

$x$ and

y

$y$

$x =$ $x=$ (6) $y =$ $y=$ (4)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

First, identify corresponding sides and angles of the two triangles.

Write out the proportions of corresponding sides to solve for $x$ $x$

$\frac{\color{#e85e00}{QP}}{\color{#e85e00}{MN}}=\frac{\color\green{x}}{\color\green{ON}}$			Definition of Similarity

$\frac{\color{#e85e00}{15}}{\color{#e85e00}{5}}=\frac{\color\green{x}}{\color\green{2}}$			Plug in the side lengths

$2 \times 15$ $2 xx 15$	$=$ $=$	$5 \times x$ $5 xx x$	Cross Multiply
$30$ $30$ $\div 5$ $divide 5$	$=$ $=$	$5 x$ $5x$ $\div 5$ $divide 5$	Divide both sides by $5$ $5$
$6$ $6$	$=$ $=$	$x$ $x$
$x$ $x$	$=$ $=$	$6$ $6$

Do the same to solve for $y$ $y$

$\frac{\color{#e85e00}{QP}}{\color{#e85e00}{MN}}=\frac{\color{#004ec4}{RP}}{\color{#004ec4}{y}}$			Definition of Similarity

$\frac{\color{#e85e00}{15}}{\color{#e85e00}{5}}=\frac{\color{#004ec4}{12}}{\color{#004ec4}{y}}$			Plug in the side lengths

$y \times 15$ $y xx 15$	$=$ $=$	$5 \times 12$ $5 xx 12$	Cross Multiply
$15 y$ $15y$	$=$ $=$	$60$ $60$
$15 y$ $15y$ $\div 15$ $divide 15$	$=$ $=$	$60$ $60$ $\div 15$ $divide 15$	Divide both sides by $15$ $15$
$y$ $y$	$=$ $=$	$4$ $4$

x = 6

$x=6$ and

y = 4

$y=4$

Question 2 of 5

The following two triangles are similar.

Solve for the missing side

y

$y$

$y =$ $y=$ (24)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

First, seperate the two triangles.

Write out the proportions of corresponding sides to solve for $y$ $y$

$\frac{\color{#e85e00}{BC}}{\color{#e85e00}{DE}}=\frac{\color\green{y}}{\color\green{AD}}$			Definition of Similarity

$\frac{\color{#e85e00}{6}}{\color{#e85e00}{2}}=\frac{\color\green{y}}{\color\green{8}}$			Plug in the side lengths

$6 \times 8$ $6 xx 8$	$=$ $=$	$2 \times y$ $2 xx y$	Cross Multiply
$48$ $48$	$=$ $=$	$2 y$ $2y$
$48$ $48$ $\div 2$ $divide 2$	$=$ $=$	$2 y$ $2y$ $\div 2$ $divide 2$	Divide both sides by $2$ $2$
$24$ $24$	$=$ $=$	$y$ $y$

y = 24

$y=24$

Question 3 of 5

The following two triangles are similar.

Solve for the missing sides

x

$x$ and

y

$y$

$x =$ $x=$ (5.88) $y =$ $y=$ (5.9)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

First, seperate the two triangles.

Write out the proportions of corresponding sides to solve for $x$ $x$

$\frac{\color{#e85e00}{AB}}{\color{#e85e00}{AE}}=\frac{AC}{\color\green{AD}}$			Definition of Similarity

$\frac{\color{#e85e00}{22}}{\color{#e85e00}{5}}=\frac{x+20}{\color\green{x}}$			Plug in the side lengths

$5 \times (x + 20)$ $5 xx (x+20)$	$=$ $=$	$22 \times x$ $22 xx x$	Cross Multiply
$5 x + 100$ $5x +100$	$=$ $=$	$22 x$ $22x$	Simplify
$100$ $100$	$=$ $=$	$17 x$ $17x$
$100$ $100$ $\div 17$ $divide 17$	$=$ $=$	$17 x$ $17x$ $\div 17$ $divide 17$	Divide both sides by $17$ $17$
$5.88$ $5.88$	$=$ $=$	$x$ $x$

Do the same on corresponding sides to solve for $y$ $y$

$\frac{\color{#e85e00}{5}}{\color{#e85e00}{22}}=\frac{\color{#004ec4}{y}}{\color{#004ec4}{26}}$			Plug in the side lengths

$22 \times y$ $22 xx y$	$=$ $=$	$5 \times 26$ $5 xx 26$	Cross Multiply
$22 y$ $22y$	$=$ $=$	$130$ $130$	Simplify
$22 y$ $22y$ $\div 22$ $divide 22$	$=$ $=$	$130$ $130$ $\div 22$ $divide 22$	Divide both sides by $22$ $22$
$y$ $y$	$=$ $=$	$5.9$ $5.9$

x = 5.88

$x=5.88$ and

y = 5.9

$y=5.9$

Question 4 of 5

The following two triangles are similar.

Solve for the missing side

x

$x$

$x =$ $x=$ (7)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

First, seperate the two triangles.

Notice that length $A B = 14$ $AB=14$ since the sum of

A E = 6

$AE=6$ and

E B = 8

$EB=8$ is

14

$14$

Write out the proportions of corresponding sides to solve for $x$ $x$

$\frac{\color{#e85e00}{AE}}{\color{#e85e00}{AB}}=\frac{\color\green{ED}}{\color\green{x}}$			Definition of Similarity

$\frac{\color{#e85e00}{6}}{\color{#e85e00}{14}}=\frac{\color\green{3}}{\color\green{x}}$			Plug in the side lengths

$6 \times x$ $6 xx x$	$=$ $=$	$3 \times 14$ $3 xx 14$	Cross Multiply
$6 x$ $6x$ $\div 6$ $divide 6$	$=$ $=$	$42$ $42$ $\div 6$ $divide 6$	Divide both sides by $6$ $6$
$x$ $x$	$=$ $=$	$7$ $7$

x = 7

$x=7$

Question 5 of 5

The following two triangles are similar.

Solve for the missing side

y

$y$

$y =$ $y=$ (4.8)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

First, seperate the two triangles.

Write out the proportions of corresponding sides to solve for $y$ $y$

$\frac{\color{#e85e00}{EB}}{\color{#e85e00}{BC}}=\frac{\color\green{AB}}{\color\green{y}}$			Definition of Similarity

$\frac{\color{#e85e00}{20}}{\color{#e85e00}{8}}=\frac{\color\green{12}}{\color\green{y}}$			Plug in the side lengths

$12 \times 8$ $12 xx 8$	$=$ $=$	$20 \times y$ $20 xx y$	Cross Multiply
$96$ $96$	$=$ $=$	$20 y$ $20y$
$96$ $96$ $\div 20$ $divide 20$	$=$ $=$	$20 y$ $20y$ $\div 20$ $divide 20$	Divide both sides by $20$ $20$
$4.8$ $4.8$	$=$	$y$

$y=4.8$

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Well Done!

2. Question

Hint

Nice Job!

3. Question

Hint

Excellent!

4. Question

Hint

Fantastic!

5. Question

Hint

Keep Going!

Quizzes