Chapter 1

Question 1

formed by two rays with the same end point

Answer 1

angle

Question 2

The common endpoint of an angle is called the

Answer 2

vertex

Question 3

The rays of an angle are called the

Answer 3

sides

Question 4

Symbol commonly used to represent an angle

Answer 4

theta θ

Question 5

Angle θ can also be denoted by AOB, where the letter associated with the vertex is written between the letters associated with the points on each side, so the vertex is

Answer 5

O

Question 6

When the rotation from the initial side to the terminal side takes place in a counterclockwise direction, the angle formed is

Answer 6

a positive angle

Question 7

If the rotation from the initial side to the terminal side is in a clockwise direction, the angle formed is

Answer 7

a negative angle

Question 8

We can think of θ as being formed by rotating side OA about the vertex to side OB. In this case, we call side OA the

Answer 8

initial side

Question 9

We can think of θ as being formed by rotating side OA about the vertex to side OB. In this case, we call side OB the

Answer 9

terminal side

Question 10

The angle formed by rotating a ray through one complete revolution has a measure of

Answer 10

360 degrees

Question 11

is 1/360 of a full rotation

Answer 11

1 degree

Question 12

Angles that measure 90 degrees are called

Answer 12

right angles

Question 13

angles that measure 180 degrees are called

Answer 13

straight angles

Question 14

Angles that measure between 0 degrees and 90 degrees are called

Answer 14

acute angles

Question 15

angles that measure between 90 degrees and 180 degrees are called

Answer 15

obtuse angles

Question 16

Two angles with a sum of 180 degrees are called

Answer 16

supplementary angles

Question 16

If two angles have a sum of 90 degrees, then they are called

Answer 16

complementary angles

Question 17

Give the complement and the supplement of each angle.
1) 40 degrees
2) 110 degrees
3) θ

Answer 17

1) 50 degrees and 140 degrees
2) -20 degrees and 70 degrees
3) 90 degrees and 180 degrees

Question 18

We denote the angles (or vertices) of a triangle with

Answer 18

uppercase letters

Question 19

We denote the lengths of the sides of a triangle with

Answer 19

lowercase letters

Question 20

It is standard practice in mathematics to label the sides and angles so that
a is opposite
b is opposite
c is opposite

Answer 20

A
B
C

Question 21

A triangle where all three sides are of equal length and all three angles are equal is called an

Answer 21

equilateral triangle

Question 22

A Triangle where all three angles are acute is called an

Answer 22

acute triangle

Question 22

A triangle that has two equal sides and two equal angles is called an

Answer 22

isosceles triangle

Question 23

If all the sides and angles are different, the triangle is called

Answer 23

scalene

Question 24

A triangle that has exactly one obtuse angle is called an

Answer 24

obtuse triangle

Question 25

A triangle that has on right angle is called a

Answer 25

right triangle

Question 26

In every right triangle, the longest side is called the

Answer 26

hypotenuse

Question 27

The hypotenuse is always opposite of the

Answer 27

right angle

Question 28

The other two sides of a right triangle (excluding the hypotenuse) are called the

Answer 28

legs

Question 29

In any right triangle in which the two acute angles are 30 degrees and 60 degrees, the side of medium length (the side opposite the 60 degrees angle) is always

Answer 29

√3 times the shortest side
shortest side = t
medium side = t√3

Question 30

Because the sum of the angles in any triangle is 180 degrees, the other two angles (legs) in a right triangle must be

Answer 30

complementary, acute angles

Question 30

the sum of the angles in any triangle is

Answer 30

180 degrees

Question 31

Pythagorean theorem formula

Answer 31

c² = a² + b²

Question 32

In any right triangle, the square of the length of the longest side (called the hypotenuse) is equal to the sum of the squares of the

Answer 32

legs

Question 33

In any right triangle in which the two acute angles are 30 degrees and 60 degrees, the longest side (the hypotenuse) is always

Answer 33

twice the shortest side (the side opposite the 30 degrees angle)
longest side = 2t
shortest side = t

Question 34

To verify the relationship between the sides in this triangle (30-60-90), we draw an

Answer 34

equilateral triangle (one in which all three sides are equal) and label half the base with t

Question 35

bisects the base to make two 30-60-90 triangles.

Answer 35

altitude h

Question 36

If the longest side of a 30-60-90 triangle is 14, find the lengths of the other two sides.

Answer 36

longest = 14
shortest = 7
medium = 7√3

Question 37

A ladder is leaning against a wall. The bottom of the ladder makes an angle of 60 degrees with the ground and is 3 feet from the base of the wall. How long is the ladder and how high up the wall does it reach?

Answer 37

ladder length = 6ft
wall height = 3

Question 38

If the shortest side of a 30-60-90 triangle is 5, find the other two sides

Answer 38

shortest = 5
longest = 10
medium = 5√3