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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.
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