Unit 1- Introduction to Geometry: Angle Relationships Notes
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Date
I can…
Essential Question(s):
Key Concepts
Adjacent angles
 Definition

What do they look like?
Vertical angles
 Definition

What do they look like?
Linear Pair
 Definition

What do they look like?
Notes
Identifying Angle Pairs Examples
a) Name two adjacent angles.
b) Name two vertical angles.
c) Name two angles that form a
linear pair.
a) Name two adjacent angles.
b) Name two vertical angles.
c) Name two angles that form a
linear pair.
Complementary angles
 Definition

What do they look like?
Supplementary angles
 Definition

What do they look like?
Angle Measure Examples
a) Find the measures of two
complementary angles if the
difference in the measures of the
two angles is 12.
b) Find the measures of two
supplementary angles if the
measure of one angle is 6 less than
five times the measure of the other
angle.
Perpendicular lines
 Definition

What do they look like?

Symbol

How do you write them?
Perpendicular Line Examples
a) Find x and y so that ⃗⃗⃗⃗⃗
𝐵𝐸 and ⃗⃗⃗⃗⃗
𝐴𝐷
are perpendicular.
b) Find x so that ⃡⃗⃗⃗⃗
𝐾𝑂  ⃡⃗⃗⃗⃗⃗
𝐻𝑀.
Interpreting Figures Examples
Based on the figure below, determine
whether each statement can be assumed
from the figure below.
1.  LPM and  MPO are adjacent
angles.
2.  OPQ and  LPM are
complementary.
3.  LPO and  QPO form a linear
pair.
Summary, Reflection, Analysis…
Unit 1 –Introduction to Geometry: Angle Relationships Exercise
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Date
1. Is it possible for two supplementary angles to both be obtuse? Explain why or why not.
Directions: Identify each pair of angles as adjacent, vertical, and/or as a linear pair.
2. ∠1 and ∠2
4. ∠1 and ∠5
3. ∠1 and ∠6
5. ∠3 and ∠2
Directions: Use the figure below to answer the following questions.
6. Name a pair of adjacent angles.
7. Name a pair of vertical angles.
8. Name a pair of angles that form a
linear pair.
9. Two angles are supplementary. One angle measures 12° more than the other. Find the measures
of the angles.
10. Find the measure of an angle and its complement if one angle measures 18 degrees more than the
other.
11. Two angles are complementary. The measure of one angle is 21 more than twice the measure of
the other angle. Find the measures of the two angles.
12.
⃡⃗⃗⃗⃗⃗ .
⃡⃗⃗⃗⃗ ⊥ 𝑀𝑄
Solve for x and y so that 𝑁𝑅
13.
⃗⃗⃗⃗⃗ ⊥ 𝑍𝑃
⃗⃗⃗⃗⃗ .
Solve for x and m ∠DZQ if 𝑍𝑃
14.
Lines p and q, which intersect to form perpendicular lines, form adjacent angles 1 and 2.
If m ∠ 1 = 3x + 18 and m ∠2 = −8𝑦 − 70, find the values of x and y. (It might help to draw a
picture first.
Directions: Determine whether each statement can be assumed from the picture. Explain why or why
not.
15. ∠WZU is a right angle.
16. ∠YZU and ∠UZV are supplementary.
17. ∠VZU is adjacent to ∠YZX.