Triangles and the Pythagorean theorem — SSAT Upper practice questions

112 practice questions in the app
Free

Practice 112 Triangles and the Pythagorean theorem questions in the app

What this topic is

Triangles and the Pythagorean theorem bring together several facts that SSAT Upper questions like to combine.

A triangle's angles add to one hundred eighty degrees, the two base angles of an isosceles triangle are equal, and an exterior angle equals the sum of the two interior angles not next to it. For right triangles, the Pythagorean theorem says the squares of the two legs add to the square of the hypotenuse, and familiar triples such as three, four, five save time.

Similar triangles have proportional sides, so their perimeters scale by the same factor. Subtracting from one hundred eighty when the exterior angle rule was needed is a typical slip.

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 $12 8^{\circ}$ . One of the two remote interior angles measures $5 7^{\circ}$ . What is the measure of the other remote interior angle?

Show answer

Answer: C — $7 1^{\circ}$

The two remote interior angles must add to $12 8^{\circ}$ . Since one is $5 7^{\circ}$ , the other is $12 8^{\circ} - 5 7^{\circ} = 7 1^{\circ}$ .

Question 2Mid

An isosceles triangle has a vertex angle of $4 4^{\circ}$ . What is the measure of each base angle?

Show answer

Answer: D — $6 8^{\circ}$

The two base angles sum to $18 0^{\circ} - 4 4^{\circ} = 13 6^{\circ}$ . Since they are equal, each base angle is $13 6^{\circ} \div 2 = 6 8^{\circ}$ .

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 $25 \div 10 = 2.5$ . 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 112 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)