IXL | Similar and congruent figures

Are these shapes congruent?

63°

117°

64°

67°

112°

117°

70 ft

39 ft

35 ft

39 ft

67 ft

39 ft

35 ft

39 ft

yes

ref_doc_title.

Learn with an example

question

Are these shapes similar?

30 mm

35 mm

30 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.

30 mm

35 mm

30 mm

First, see if the corresponding angles are all congruent.

O	≅	U

P	≅	V

Q	≅	W

R	≅	T

The corresponding angles are all congruent.

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

OPQR is a square. All the sides are the same length. PQ and QR are both 30 mm.

UVWT is a rectangle. The opposite sides are congruent. UV is 35 mm and VW is 30 mm.

OP and UV have a ratio of

, which is equivalent to

PQ and VW have a ratio of

, which is equivalent to

QR and WT have a ratio of

, which is equivalent to

RO and TU have a ratio of

, which is equivalent to

The ratios are not all the same, so the corresponding sides are not proportional.

Since the corresponding sides are not proportional, the shapes are not 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

X.1Find the constant of proportionality from a table

L.10Do the ratios form a proportion?

Lesson: Similarity

Lesson: Congruence

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