Transcript Lesson 1 Contents - Headlee's Math Mansion

Lesson 1-5
Angle Relationships
Transparency 1-5
5-Minute Check on Lesson 1-4
G
Refer to the figure for questions 1 through 5.
1. Name the vertex of 3.
B
A
2. Name a point in the interior of ACB.
3. Name the sides of BAC
D
3
C
4. Name an acute angle with vertex B
5. If BD bisects ABC, m ABD = 2x + 5 and m DBC = 3x – 16, find
m ABD.
6.
If P is in the interior of MON and
m MOP = ½ m MOP, what can you conclude?
Standardized Test Practice:
A
PON  NOM
B
MON is an acute angle
C
m MOP > m PON
D
OP is the angle bisector of MON
Click the mouse button or press the
Space Bar to display the answers.
Transparency 1-5
5-Minute Check on Lesson 1-4
G
Refer to the figure for questions 1 through 5.
1. Name the vertex of 3.
C
A
2. Name a point in the interior of ACB.
3. Name the sides of BAC
B
G
D
BA, AC
4. Name an acute angle with vertex B ABD or DBC
3
C
5. If BD bisects ABC, m ABD = 2x + 5 and m DBC = 3x – 16, find
m ABD. 2x + 5 = 3x – 16
x = 21
m ABD = 47
6.
If P is in the interior of MON and
m MOP = ½ m MOP, what can you conclude?
Standardized Test Practice:
A
PON  NOM
B
MON is an acute angle
C
m MOP > m PON
D
OP is the angle bisector of MON
Click the mouse button or press the
Space Bar to display the answers.
Objectives
• Identify and use special pairs of angles
• Identify perpendicular lines
Vocabulary
• Adjacent angles – two coplanar angles that have a common
vertex, a common side, but no common interior points
• Linear pair – a pair of adjacent angles whose noncommon sides
are opposite rays (always supplementary)
• Vertical angles – two non adjacent angles formed by two
intersecting lines
Vertical angles are congruent (measures are equal)!!
• Complementary Angles – two angles whose measures sum to 90°
• Supplementary Angles – two angles whose measures sum to 180°
• Perpendicular – two lines or rays are perpendicular if the angle (s)
formed measure 90°
Angles
360º
A
Exterior of angle
Circle
Vertex
(point V)
Interior of angle
AVB or V
V
B
Ray VB
Angles measured in degrees
A degree is 1/360th around a circle
Acute
A
mA < 90º
Right
Obtuse
A
A
mA = 90º
90º < mA < 180º
Names of angles: Angles have 3 letter names (letter on one side, letter of the
vertex, letter on the other side) like AVB or if there is no confusion, like in most
triangles, then an angle can be called by its vertex, V
Name two angles that form a linear pair.
A linear pair is a pair of
adjacent angles whose
noncommon sides are
opposite rays.
Answer: The angle pairs that satisfy this definition are
Name two acute vertical angles.
There are four acute
angles shown. There is one
pair of vertical angles.
Answer: The acute vertical angles are VZY
and XZW.
Name an angle pair that satisfies each condition.
a. two acute vertical angles
Answer: BAC and FAE,
CAD and NAF, or
BAD and NAE
b. two adjacent angles whose
sum is less than 90
Answer: BAC and CAD or
EAF and FAN
ALGEBRA Find the measures of two supplementary
angles if the measure of one angle is 6 less than five
times the other angle.
Explore
The problem relates the measures of two
supplementary angles. You know that the sum
of the measures of supplementary angles is 180.
Plan
Draw two figures to represent the angles.
Let the measure of one angle be x.
Solve
Given
Simplify.
Add 6 to each side.
Divide each side by 6.
Use the value of x to find each angle measure.
Examine Add the angle measures to verify that the
angles are supplementary.
Answer: 31, 149
ALGEBRA Find x and y so that
are perpendicular.
and
AD  CE  4 right angles
sum of parts = whole
4x° + 5x° = 90°
9x° = 90°
x = 10°
(7y – 15)° = 90°
7y° = 105°
y = 15°
Answer: x = 10° y = 15°
Summary & Homework
• Summary:
– There are many special pairs of angles such as
adjacent angles,
vertical angles,
complementary angles,
supplementary angles,
and linear pairs.
• Homework:
– pg 41-43; 11-16, 21, 32-33, 44-49