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DRILL
Angles
* An angle is made up of two rays that share
the same endpoint.
A
B
C
B
ABC
•To name an angle we either
can use the one point where
the vertex is located if there is
only one angle, otherwise we
must use three points making
sure the vertex is in the
middle.
Naming Angles
E
D
A
C
B
1.4
Measuring Angles
& Segments
Notes(Vocab)
Ruler Postulate: the distance
between any two points is the
absolute value of the difference.
Congruent: Is the term used in
Geometry to describe two
shapes or objects which are
Equal.
Segment Addition Postulate:
If three points A, B, and C are
collinear and B is between A
and C, then AB + BC =AC.
A
B
C
Measuring Angles: an angle
measure is found by taking the
absolute value of the difference
of each angle.
Angle Addition Postulate: If
two angles share a common
ray then the sum of those two
angles is equal to the larger
angle.
B
C
A
D
Drill
1) Draw a segment so that A and C are
the endpoints and B is somewhere
between them.
2) If AB is 10 feet and BC is 18 feet,
how long is AC?
3) If AB is 2x feet and BC is 3x + 4
feet and AC is 39 feet how long is
AB?
1.5
Good Definitions
What is a Polyglob?
Properties of Good Definitions
• Uses clearly understood terms,
meaning they should be commonly
understood or previously defined.
• Is Precise, Avoid words such as large,
sort of, and some.
• States what the term is, rather then
what it is not.
Ex: Big is the opposite of small.
Midpoint: is the point that divides a
segment into two congruent parts.
Perpendicular Lines: are lines that
intersect to make a right angle.
Perpendicular Bisector: is a
perpendicular line that passes
through the mid point of a segment.
Angle Bisector: is a ray that divides
an angle into two congruent parts.
Drill
1)
A
B
C
If AB is 15 and AC is 80 find BC.
2) Is this a good definition? Explain
An apple is a fruit that is not an orange.
3) 30, 26, 21, 15, ___, ___, ___
A
B
C
If AB is 15 and AC is 80 find BC.
80 – 15 = 65 therefore BC = 65
An apple is a fruit that is not an orange.
No, b/c of the word NOT being used.
3) 30, 26, 21, 15, 8, 0, -9
1.6 Basic Constructions
Objective: The students will be able to
construct perpendicular bisectors and angle
bisectors, as well as understand their properties.
Tools For Constructions
• Compass
• Straightedge
• Patty Paper
• Geometer’s
Sketchpad
Perpendicular Bisector
• Is a line that is perpendicular to a segment
and passes through the midpoint.
Steps for Construction/Patty Paper
a) Trace the segment on the patty paper.
b) Label Endpoints
c) Fold paper so that the two endpoints match
up and unfold.
d) Trace the fold to create your perpendicular
bisector
Fold
A
M
B
Angle Bisector
• Is a ray that cuts an angle into two congruent
angles.
Steps for Construction/Patty Paper
a) Trace the angle on the patty paper
b) Label Points
c) Pinch the vertex and fold the paper so that
the two rays that create the angle match up
and unfold
d) Trace the fold to create your angle bisector
C
Fold
E
D
A
B
Summary
• Constructed Perpendicular and Angle
Bisectors
• Found measures using both types of bisectors
• Creating angle bisectors will lead us into
vertical angles as well as linear angles.
Drill
1) A
B
C
If AB is 3x and BC is 2x + 10, find BC
if AC equals 80 feet.
2) Does the ceiling and your desktop
represent parallel planes? (WHY)
3) How many and what type of points
do we need to name a plane?
1.7
Using Deductive Reasoning
Types of Angles
Vertical Angles
Vertical Angles are angles that are opposite each
other where two lines intersect.
Ex : 1 & 3 as well as 2 & 4
Types of Angles
Adjacent Angles
Adjacent Angles are angles that share a common
endpoint and share a common ray.
Ex : Angles A and B
Types of Angles
Complementary Angles
Two angles that have a sum
of 90 degrees.
Types of Angles
Supplementary Angles
Two angles that have a sum
of 180 degrees.
Guided Practice
Guided Practice
Guided Practice
Homework
Worksheet # 1.7
1.8
The Coordinate Plane
Formulas
The Distance Formula
d  ( x2  x1 )  ( y2  y1 )
2
2
Midpoint Formula
 x1  x2 y1  y2 
,


2 
 2