IXL - Side lengths in similar triangles (Geometry practice)

or

△

S

T

U

~

△

B

A

C

.

Find

B

C

.

14

14

24

S

T

U

28

B

A

C

B

C

=

ref_doc_title.

or

Learn with an example

question

△

F

G

H

~

△

U

T

V

.

Find

F

H

.

28

40

F

G

H

7

10

9

U

T

V

F

H

=

key idea

Two polygons are similar if and only if their corresponding angles are congruent and their corresponding sides are proportional.

solution

Use the fact that

F

G

H

is similar to

U

T

V

to write proportions and solve for

F

H

.

△

F

G

H

~

△

U

T

V

28

40

F

G

H

7

10

9

U

T

V

To start, find two corresponding sides whose lengths are given:

F

G

=

28

and

T

U

=

7

.

Now write the proportions.

Write a proportion to solve for

F

H

. Use

F

G

,

T

U

,

F

H

, and its corresponding side

U

V

.

F

G

T

U

=

Definition of similarity

F

H

U

V

Definition of similarity

28

7

=

Plug in

F

G

=

28

,

T

U

=

7

,

and

U

V

=

9

F

H

9

Plug in

F

G

=

28

,

T

U

=

7

,

and

U

V

=

9

4

=

Simplify

F

H

9

Simplify

36

=

Multiply both sides by 9

F

H

Multiply both sides by 9

So,

F

H

=

36

.

Looking for more? Try these:

Lesson: Similarity

Lesson: Similar triangles

or

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Excellent!

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Identify similar triangles

G.1Solve proportions

Lesson: Similarity

Lesson: Similar triangles