Name: ______________________ Date: _________________

Foundations of Mathematics 11

Chapter 2- Angles & Triangles Lesson #1 - Introduction/Review of Geometry

Before we get into parallel lines, let’s review some things we’ve learned about angles in previous years:

Part 1 – Angle Identification

An angle may be named in 3 ways: There are 3 angles shown here:

_______ _______ or _______

_______ _______ or _______

_______ _______ or _______

When there is more than one angle meeting

at the same vertex ( ____ ) , we don’t name it with a

single letter.

Part 2 – Angle Classification

Angles can be classified into 6 groups. They are classified by their angle measures.

An _________ angle A ________ angle An __________ angle

is less than 90o equals exactly 90o is between 90o and 180o

A ____________ angle A __________ angle A complete rotation is equals

exactly 180o is between 180o and 360o 360o

Part 3 – Properties of Angles Congruence Property: angles with the same measurement and congruent

Note that X = _______ o and Y = _______ o

If 2 angles are equal in measure, we would indicate

this on the drawings as shown.

Addition Property: the sum of a larger angle can be determined by adding 2 or more

smaller angles with given angle measures.

Note that _______ + _______ = SUM

Example 1: Use the angle properties to solve:

Part 4 – Complementary and Supplementary Angles

Complementary angles have a combined measure of ______ .

FIG = _______ o and GIJ = _______ o

Example 2: Write the measure of the complementary angle.

(a) 44_____ (b) 7

_____ (c) 66

_____ (d) 45

_____

Name the complementary angle for each angle.

CAB _______ LAK _______

LAM _______ GAF _______

FAB _______ JAM _______

CAK _______

Supplementary angles have a combined measure of ______ .

Example 3: Write the measure of the supplementary angle.

(a) 57_____ (b) 101

_____ (c) 165

_____

Determine the angle that would be supplementary to the angles shown.

Part 5 – Vertically Opposite Angles

Vertically Opposite Angles are the angles opposite each other when two lines cross.

Use a protractor to measure each of the following angles:

n= _____

e = _____

s = _____

w = _____

_____

_____

_____

_____

a

b

c

d

Write a conjecture about the relationship of opposite angles at the same vertex:

d

c

b

a

Example 4: Without using a protractor, find the measures of the missing angles.

Part 6 – Angles at a Point

Measure each of the following angles:

a = __________

b = __________

c = __________

d = __________

Sum =

Write a conjecture about the sum of angles at a point:

This property is generally used with all of the rules we reviewed thus far.

Example 5: Determine the measure of the missing angles.