Triangles and the Pythagorean theorem — SSAT Upper practice questions

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Practice 108 Triangles and the Pythagorean theorem questions in the app

What this topic is

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.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

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

61^\circ

✗ Not this one

67^\circ

✗ Not this one

71^\circ

✓ Correct

75^\circ

✗ Not this one

81^\circ

✗ Not this one

Show answer

Answer: C — $71^\circ$

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

Question 2Mid

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

44^\circ

✗ Not this one

58^\circ

✗ Not this one

62^\circ

✗ Not this one

68^\circ

✓ Correct

72^\circ

✗ Not this one

Show answer

Answer: D — $68^\circ$

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

Question 3Mid

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?

Show answer

Answer: C — 60

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

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 108 Triangles and the Pythagorean theorem questions in the app

Triangles and the Pythagorean theorem — SSAT Upper practice questions

What this topic is

Sample questions

More SSAT Upper topics

Quantitative (Math)