Question 1

Which of the following best describes an isosceles triangle?

Accepted Answer

A triangle with at least two sides of equal length.

Question 2

Given a right triangle with legs of length $$a = 5$$ and $$b = 12$$, what is the length of the hypotenuse $$c$$?

Accepted Answer

$$c = 13$$

Question 3

Which of the following statements about similar triangles is TRUE?

Accepted Answer

Similar triangles have equal corresponding angles.

Question 4

A triangle has angles measuring $$30^\circ$$, $$60^\circ$$, and $$90^\circ. If $$the shortest side has length $$4$$, what is the length of the hypotenuse?

Accepted Answer

$$8$$

Question 5

Which of the following is a Pythagorean triple?

Accepted Answer

$$(6, 8, 10)$$

Question 6

If two triangles are similar and the proportionality constant $$k = 3$$, and a side of the smaller triangle is $$5$$, what is the length of the corresponding side in the larger triangle?

Accepted Answer

$$15$$

Question 7

Which triangle has all three sides congruent and all angles measuring $$60^\circ$$?

Accepted Answer

Equilateral triangle

Question 8

A right triangle has legs of length $$a$$ and $$b$$, and hypotenuse $$c. $$Which equation must always be true?

Accepted Answer

$$a^2$$ + $$b^2$$ = $$c^2$$

Question 9

A triangle has sides of length $$7$$, $$24$$, and $$25. Is $$this triangle a right triangle?

Accepted Answer

Yes, because $$7^2$$ + $$24^2$$ = $$25^2$$

Question 10

Which of the following best describes a scalene triangle?

Accepted Answer

A triangle with all sides of different lengths.

Question 11

If two triangles are similar and the sides of the smaller triangle are $$3$$, $$4$$, and $$5$$, and the proportionality constant is $$2$$, what are the side lengths of the larger triangle?

Accepted Answer

$$6$$, $$8$$, $$10$$

Question 12

In a $$45^\circ$$-$$45^\circ$$-$$90^\circ$$ triangle, if the length of one leg is $$x$$, what is the length of the hypotenuse?

Accepted Answer

$$x\sqrt{2}$$

Question 13

A triangle has angles measuring $$100^\circ$$, $$40^\circ$$, and $$40^\circ. $$How would you classify this triangle by its angles?

Accepted Answer

Obtuse triangle

Question 14

Which of the following is NOT a property of similar triangles?

Accepted Answer

Corresponding sides are equal in length.

Question 15

A triangle has sides of length $$8$$, $$15$$, and $$17. Is $$this a right triangle?

Accepted Answer

Yes, because $$8^2$$ + $$15^2$$ = $$17^2$$

Question 16

In a $$30^\circ$$-$$60^\circ$$-$$90^\circ$$ triangle, if the hypotenuse is $$10$$, what is the length of the side opposite the $$30^\circ$$ angle?

Accepted Answer

$$5$$

Question 17

Which of the following triangles CANNOT be classified by its sides as isosceles?

Accepted Answer

A triangle with sides $$5$$, $$7$$, $$9$$

Question 18

If the sides of a triangle are $$9$$, $$12$$, and $$15$$, what is the proportionality constant $$k$$ compared to the $$3$$-$$4$$-$$5$$ triangle?

Accepted Answer

$$k = 3$$

Question 19

Which of the following is TRUE about the angles of an equilateral triangle?

Accepted Answer

Each angle measures $$60^\circ.$$

Question 20

A triangle has sides $$a = 6$$, $$b = 8$$, and $$c = 10. Is $$this triangle similar to a $$3$$-$$4$$-$$5$$ triangle?

Accepted Answer

Yes, because the sides are proportional with $$k = 2$$

Triangles and Their Properties in Precalculus

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