Triangle Similarity and Ratios

The video tutorial explores the concept of triangle similarity, focusing on comparing triangles DEF, GHI, and JKL with triangle ABC. It explains how to determine similarity using congruent angles and side ratios. The tutorial uses coordinate geometry and the Pythagorean theorem to calculate side lengths and verify similarity. All triangles are found to be similar to ABC, with detailed calculations and explanations provided for each comparison.

What is one of the key conditions for two triangles to be similar?

• They must have the same area.

• They must have the same perimeter.

• They must be right triangles.

• They must have corresponding congruent angles.

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CCSS.HSG.CO.B.7

When comparing triangle JKL to triangle ABC, which side of JKL corresponds to side BC of ABC?

• Side JL

• Side JK

• Side KL

• Side KJ

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CCSS.8.G.B.8

What is the length of side KJ in triangle JKL?

• Square root of 18

• 3 square roots of 2

• 3 square roots of 10

• 2 square roots of 10

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CCSS.HSG.GPE.B.7

What is the length of side KL in triangle JKL?

• 2 square roots of 10

• 3 square roots of 2

• Square root of 18

• 3 square roots of 10

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CCSS.HSG.SRT.A.2

What is the ratio of the sides BC and EF in triangles ABC and DEF?

• 4

• 3

• 2

• 1

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CCSS.HSG.CO.B.7

Which side of triangle GHI corresponds to side BC of triangle ABC?

• Side GH

• Side HG

• Side HI

• Side IG

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CCSS.HSG.GPE.B.7

What is the length of side HI in triangle GHI?

• 2 square roots of 2

• 3 square roots of 2

• Square root of 8

• 2 square roots of 10

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CCSS.HSG.SRT.A.2

What is the ratio of the sides BA and HG in triangles ABC and GHI?

• 4/3

• 3/2

• 2/3

• 1/2

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CCSS.HSG.SRT.A.2

Which of the following triangles is not similar to triangle ABC?

• Triangle DEF

• All are similar

• Triangle GHI

• Triangle JKL

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What theorem is used to calculate the side lengths of the triangles?

• Cosine rule

• Pythagorean theorem

• Sine rule

• Thales' theorem

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11