IXL | Identify similar quadrilaterals

Are these shapes similar?

35 yd

26 yd

18 yd

26 yd

35 yd

28 yd

17 yd

28 yd

yes

ref_doc_title.

Learn with an example

question

Are these shapes similar?

24 yd

27 yd

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.

24 yd

27 yd

First, see if the corresponding angles are all congruent.

C	≅	T

B	≅	U

A	≅	R

D	≅	S

The corresponding angles are all congruent.

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

CBAD is a square. All the sides are the same length. AD and DC are both 24 yd.

TURS is also a square. All the sides are the same length. UR and RS are both 27 yd.

CB and TU have a ratio of

, which is equivalent to

BA and UR have a ratio of

, which is equivalent to

AD and RS have a ratio of

, which is equivalent to

DC 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

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Lesson: Similarity

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