Similar Triangles and Proportions: Geometry Math Test – PDF Download

Question 1: Similarity by SAS (2 points)

In the figure, \(AB=8,\ AC=12,\ DE=12,\ DF=18\) and \(m\angle A=m\angle D=65^{\circ}\).

1. Are the triangles similar? Name the criterion. (1 point)
2. Write a similarity statement and the scale factor from ABC to DEF. (1 point)

Question 2: Similar by SSS (2 points)

Decide whether each pair of triangles, given by side lengths, is similar. Justify each answer.

1. 9, 12, 15 and 12, 16, 20 (1 point)
2. 5, 6, 7 and 10, 12, 15 (1 point)

Question 3: Triangle proportionality (3 points)

In triangle ABC, \(DE\) ∥ \(BC\). Use the figure.

1. Find \(EC\). (1 point)
2. Find \(DE\). (1 point)
3. Name the similarity criterion that shows triangle ADE is similar to triangle ABC. (1 point)

Question 4: Converse of the side-splitter theorem (2 points)

Points D and E lie on sides AB and AC of triangle ABC. Decide whether DE is parallel to BC.

1. \(AD=6,\ DB=10,\ AE=9,\ EC=15\) (1 point)
2. \(AD=5,\ DB=7,\ AE=8,\ EC=11\) (1 point)

Question 5: Right triangle altitude (3 points)

Triangle ABC has a right angle at C, and CD is the altitude to the hypotenuse. \(AD=4\) and \(DB=16\). Find each length in simplest radical form.

1. \(CD\) (1 point)
2. \(AC\) (1 point)
3. \(BC\) (1 point)

Question 6: Complete a similarity proof (3 points)

In the figure, segments AE and BD intersect at C, and \(AB\) ∥ \(DE\). Write a reason for each step to prove that triangle ABC is similar to triangle EDC.

Question 7: Indirect measurement (2 points)

A 6 foot tall person casts an 8 foot shadow at the same time that a flagpole casts a 36 foot shadow. Use similar triangles to find the height of the flagpole.

1. Write a proportion. (1 point)
2. Solve it. (1 point)

Question 8: Similar triangles and algebra (2 points)

Triangle PQR is similar to triangle STU with \(PQ=x+2,\ QR=9,\ ST=10\) and \(TU=15\). Find \(x\) and \(PQ\).

Question 9: Geometric mean (1 point)

Find the geometric mean of 5 and 20.

⬇ Download the Geometry Similar Triangles and Proportions test (PDF, 92 KB)

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