Dorchester-02-04-2025-Similar Triangles Assessment

Triangles EFG and RST are similar. FG:ST = 3:12, and RS = 156, what is the length of EF?

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Mathematical Equivalence

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Triangles JKL and PQR are similar. The length of the sides of JKL are 5x - 155, x + 47, and x + 71. The perimeter of JKL is 306. The length of the longest side of PQR is 151 + x, what is the perimeter of PQR?

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Triangles HIJ and OPQ are similar. The length of the sides of HIJ are 79x - 6, 76 + 2x, and 154 + x. The perimeter of HIJ is 388. The length of the smallest side of OPQ is 190 + 5x, what is the length of the longest side of OPQ?

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Triangles FGH and OPQ are similar. FH:OQ = 7:11, and OP = 385, what is the length of FG?

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A tree 37 1/2 feet tall casts a shadow 80 feet long. Brad is 3 3/4 feet tall. How long is Brad's shadow?

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In right ABC, is the altitude to hypotenuse . If DB = 7 and AD = 8, find CD.

• 15

• 1

Mary claims that the triangles below are similar by angle-angle (AA). Do you agree or disagree with Mary?

• Agree, because there are two pairs of congruent angles.

• Disagree, because we can't determine if the sides are proportional.

• Disagree, because the two given angles are not congruent.

• Agree, because the triangles look similar.

Is triangle ABC similar to triangle DEF?

• No, because the corresponding sides are not proportional.

• No, because we don't know if the included angles are congruent.

• Yes, by SSS

• Yes, by SAS

Josh claims that these triangles are similar by SSS. Do you agree or disagree with Josh?

• Agree, because the triangles have a pair of congruent sides.

• Agree, because all of the ratios for the corresponding sides are equal.

• Disagree, because we cannot determine similarity without knowing the angle measures.

• Disagree, because all of the ratios for the corresponding sides are not equal.

Conclude whether triangle BEN is similar to triangle MAT.

• Yes, by SAS

• Yes, by AAA

• Yes, by AA

• Yes, by SSS