Exploring Similar Polygons and Triangles

Which of the following pairs of polygons are similar?

• Two rectangles with side lengths 4 cm by 6 cm and 8 cm by 12 cm

• Two pentagons with side lengths 4cm, 5cm to 8cm, 12cm

• Two triangles with side lengths 3 cm, 4 cm, 5 cm to 6 cm, 12 cm, 20 cm

• Two hexagons with side 2cm, 3cm to 6cm, 9cm

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CCSS.8.G.A.2

CCSS.HSG.CO.B.6

• 6 cm

• 8 cm

• 9 cm

• 12 cm

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CCSS.HSG.SRT.A.2

What is the scale factor of two similar polygons if one has a side length of 15 cm and the corresponding side of the other is 10 cm?

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CCSS.7.G.A.1

Fill in the blank: Two triangles are similar if they have two corresponding angles that are _______.

• equal

• different

• complementary

• supplementary

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CCSS.HSG.SRT.A.2

Which of the following is a correct method to prove that two triangles are similar?

Hint there are 3

• AA (Angle-Angle)

• ASA (Angle-Side-Angle)

• AAS (Angle-Angle-Side)

• SSS(SIde-Side-Side)

• SAS (Side-Angle-SIde)

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CCSS.HSG.SRT.B.5

• 24 cm

• 26 cm

• 20 cm

• 22 cm

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CCSS.HSG.SRT.A.2

Fill in the blank: The Side-Side-Side (SSS) similarity criterion states that if the corresponding side lengths of two triangles are ________, then the triangles are similar.

• equal

• proportional

• complementary

• supplementary

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CCSS.HSG.SRT.B.5

Which of the following sets of side lengths can form two similar triangles?

• 3 cm, 4 cm, 5 cm and 6 cm, 8 cm, 10 cm

• 5 cm, 12 cm, 13 cm and 10 cm, 15 cm, 20 cm

• 7 cm, 24 cm, 25 cm and 14 cm, 48 cm, 50 cm

• 8 cm, 15 cm, 17 cm and 16 cm, 30 cm, 34 cm

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CCSS.8.G.A.2

CCSS.HSG.CO.B.6

If two triangles are similar by the SAS (Side-Angle-Side) criterion, which of the following must be true?

• Two sides are equal, and the included angle is equal.

• Two sides are proportional, and the included angle is equal.

• Two angles are equal, and the included side is proportional.

• Two sides are proportional, and the included angle is complementary.

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CCSS.HSG.SRT.B.5

Determine if triangles are similar. If yes, state how (by AA, SSS, or SAS) and complete the similarity statement.

Similar by: ​ (a)  

ΔJKN ~ Δ​ (b)  

• SAS
• AA
• SSS
• Not Similar
• RVN
• VNR
• NVR
• VRN

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CCSS.HSG.SRT.A.2