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Triangles and the Pythagorean theorem — SSAT Upper practice questions

On the SSAT Upper Quantitative (Math) section, Triangles and the Pythagorean theorem covers interior and exterior angle relationships, isosceles and similar triangles, and right triangles whose sides satisfy the Pythagorean theorem. Students must find a missing remote interior angle, find each base angle of an isosceles triangle from the vertex, and use a scale factor between similar triangles to find a perimeter. Items are multiple choice with five numeric options, usually a degree measure or a length. Common traps are adding instead of subtracting to get the remote angle, splitting the vertex rather than the base, and scaling only the longest side instead of all three sides.

  • Section: Quantitative (Math) 50 questions on the paper
  • 101 practice questions in the app

Sample questions

Question 1

An exterior angle of a triangle measures 128∘128^\circ. One of the two remote interior angles measures 57∘57^\circ. What is the measure of the other remote interior angle?

  1. A61∘61^\circ
  2. B67∘67^\circ
  3. C71∘71^\circ
  4. D75∘75^\circ
  5. E81∘81^\circ
Show answer

Answer: C — 71∘71^\circ

The two remote interior angles must add to 128∘128^\circ. Since one is 57∘57^\circ, the other is 128∘−57∘=71∘128^\circ-57^\circ=71^\circ.

Question 2

An isosceles triangle has a vertex angle of 44∘44^\circ. What is the measure of each base angle?

  1. A44∘44^\circ
  2. B58∘58^\circ
  3. C62∘62^\circ
  4. D68∘68^\circ
  5. E72∘72^\circ
Show answer

Answer: D — 68∘68^\circ

The two base angles sum to 180∘−44∘=136∘180^\circ-44^\circ=136^\circ. Since they are equal, each base angle is 136∘÷2=68∘136^\circ\div2=68^\circ.

Question 3

The side lengths of a triangle are 6, 8, and 10. A similar triangle has longest side length 25. What is the perimeter of the similar triangle?

  1. A48
  2. B50
  3. C60
  4. D64
  5. E72
Show answer

Answer: C — 60

The scale factor is 25÷10=2.525\div10=2.5. The original perimeter is 6+8+10=246+8+10=24, so the similar triangle has perimeter 24(2.5)=6024(2.5)=60.

Practice 101 Triangles and the Pythagorean theorem questions in the app

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