IXL | Similar and congruent figures

Are these shapes similar?

750 in

1250 in

1000 in

1200 in

750 in

yes

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Learn with an example

question

Are these shapes similar?

18 mm

22 mm

yes

key idea

Shapes are similar if their corresponding angles are all congruent and their corresponding sides are proportional.

solution

Look for the parts that appear to be corresponding. Rotate the second shape so that it matches the first shape.

18 mm

22 mm

First, see if the corresponding angles are all congruent.

E	≅	T

D	≅	U

C	≅	V

F	≅	S

The corresponding angles are all congruent.

Next, see if the corresponding sides are proportional. Start by finding the lengths of all the sides.

ED and TU have a ratio of

, which is equivalent to

DC and UV have a ratio of

, which is equivalent to

CF and VS have a ratio of

, which is equivalent to

FE and ST have a ratio of

, which is equivalent to

The ratios are all

, so the corresponding sides are proportional.

Since the corresponding angles are all congruent and the corresponding sides are proportional, the shapes are similar.

Looking for more? Try these:

Lesson: Similarity

Lesson: Congruence

$Confetti$

Excellent!

Now entering the Challenge Zone—are you ready?

Teacher tools

Work it out

Not feeling ready yet? These can help:

Y.1Name, measure, and classify angles

Y.2Lines, line segments, and rays

N.1Find the constant of proportionality from a table

L.10Do the ratios form a proportion?

Lesson: Similarity

Lesson: Congruence

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