UNIT 1 NOTES
Lesson 1 – Points, Lines, Planes, and Postulates
GEOMETRY A
I Can…
1.
2.
3.
4.
The most basic figures in geometry are the point, line, and plane.
They are considered to be undefined terms, which cannot be defined by using other figures.
TERM
NAME
Point
Line
Plane
Points that lie on the same line are collinear. Points that lie
on the same plane are coplanar.
The points A, B, C, and D are coplanar. The points A, B, C,
and E are noncoplanar.
DIAGRAM
UNIT 1 NOTES
GEOMETRY A
TERM
NAME
DIAGRAM
Segment
Endpoint
Ray
Opposite
Rays
Pay careful attention on how to do the following:
▪ which symbols to use when naming a line, a segment, a ray
▪ the order of the letters when naming a ray
▪ the different ways to name a line and a plane
A postulate is
.
Take this time to COPY the postulates found on pages 7 and 8 onto your Unit 1 Postulate
Sheet…copy them just as they are written, and include any pictures.
UNIT 1 NOTES
Lesson 2- Segments
GEOMETRY A
I Can…
2.
6.
The distance along a line is undefined until a unit
distance (such as inches or centimeters) is
chosen. It is found by taking the absolute value of
the difference of the numbers at the endpoints.
This is also known as the length of a segment.
A
B
The length of AB , also denoted AB as the distance between A and B.
AB =
Congruent segments are segments that
denoted
.
Tick Marks are used to show congruent segments. Write two true statements about the diagram
above.
What is congruent?
What is equal?
The midpoint M of AB is
.
A segment bisector is
.
Draw a sketch here:
Write the Segment Addition Postulate on your postulate sheet.
UNIT 1 NOTES
GEOMETRY A
Connecting Algebra and Geometry
For each problem,
1. Make a sketch of situation and label appropriately.
2. Write a true geometric statement.
3. Substitute the algebraic expressions into that geometric statement.
4. Solve for the variable.
5. Substitute that variable into each algebraic expression to find the missing lengths.
Problem #1
S is between R and T. RS  2x  7 ,
ST  28 , and RT  4 x .
Find RS , ST , and RT .
Problem #2
B is the midpoint of AC , AB  5x , and
BC  3x  4 . Find AB , BC, and AC.
UNIT 1 NOTES
GEOMETRY A
Lesson 3 – Angles
I Can…
2.
6.
7.
TERM
NAME
DIAGRAM
Angle
The interior of an angle is
.
The exterior of an angle is
.
You cannot name an angle just by its vertex, if the point is the vertex of more than one
angle. In this case, you must use three points to name the angle.
E
1
D
2
H
F
Give two other names for 1 .
The measure of an angle is usually given in degrees.
UNIT 1 NOTES
GEOMETRY A
Acute Angle
Right Angle
Obtuse Angle
Straight Angle
Find the measure of each angle. Then classify.
a. WXV
b. ZXW
Congruent angles are
.
Arc Marks are used to show that two angles are congruent. Write two true statements about the
diagram above.
What is congruent?
What is equal?
An angle bisector is
.
In the diagram,
bisects
; thus
.
What is congruent?
Write the Angle Addition Postulate on your postulate sheet.
UNIT 1 NOTES
Connecting Algebra to Geometry
Remember the steps?
Problem #1
D is in the interior of ABC .
mABD  67 and mABC  105 .
Find mDBC .
Problem #3
BD bisects ABC , mABD  (6x  3) ,
and mDBC  (8 x  7) . Find mABD ,
mDBC , and mABC .
GEOMETRY A
Problem #2
T is in the interior of PQR .
mPQR  (10 x  7) , mRQT  (5x ) , &
mPQT  (4 x  6) . Find mPQT ,
mRQT , and mPQR .
UNIT 1 NOTES
GEOMETRY A
UNIT 1 NOTES
Lesson 4 – Angle Pairs
GEOMETRY A
I Can…
2.
8.
Adjacent angles are
.
Draw an example:
Draw a non-example:
A linear pair is
.
Draw an example:
Draw a non-example:
Tell whether the angle pairs are only adjacent, adjacent and form a linear pair, or not adjacent.
a. AEB and BED
Complementary Angles are
b. AEB and BEC
c. DEC and AEB
.
Such as:
Supplementary Angles are
Such as:
.
UNIT 1 NOTES
What is the complement of F ?
GEOMETRY A
What is the supplement of F ?
Two angles are supplementary. One of the angles is three times the measure of the other. What
are the measures of the two angles?
Vertical Angles are
.
Name the pairs of vertical angles in the diagram to the
right.
Below, are 5 and 7 vertical angles? Why or why not?
5
Name the pairs of vertical angles.
UNIT 1 NOTES
Lesson 5 – Parallel, Perpendicular, Skew
GEOMETRY A
I Can…
9.
10.
11.
Parallel Lines:
Perpendicular Lines:
Skew Lines:
Parallel planes:
Ex.
Given the diagram to the right, identify:
a. a pair of parallel segments
b. a pair of skew segments
c. a pair of perpendicular segments
d. a pair of parallel planes
Slopes of Parallel and Perpendicular Lines (Algebra Review)
If two lines are parallel, their slopes are
If two lines are perpendicular, their slopes are
.
.
UNIT 1 NOTES
Ex.
GEOMETRY A
Use the slopes to determine if the segments with the given endpoints are parallel,
perpendicular, or neither. Show work that verifies your answer.
y
GH and IJ , given that G(–3, –2), H(1,2),
5
4
I(–2,4), J(2, –4)
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
Write the Parallel Postulate on your Postulate Sheet.
1
2
3
4
5
x
UNIT 1 NOTES
Lesson 6 – Midpoint and Distance Formulas
GEOMETRY A
I Can…
12.
13.
Finding a Midpoint:
Suppose you have a segment, and you know the coordinates of the endpoints. Can you find the
coordinate that is the midpoint of the segment?
Formula:
y
Find the coordinates of the midpoint of PQ with
endpoints P(–8, 3) and Q(–2, 7).
10
8
6
4
2
–10
–8
–6
–4
–2
2
–2
–4
–6
–8
–10
Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).
4
6
8
10
x
UNIT 1 NOTES
Finding Distance:
GEOMETRY A
Suppose you have two points in the coordinate plane, and you
connect them to make a segment. What is the distance
between those two points?
y
10
8
6
Formula:
4
2
–10
–8
–6
–4
–2
2
4
6
–2
–4
–6
–8
–10
Use the Distance Formula to find the distance from the 2 points below. Round to the nearest
tenth, if necessary.
D(3, 4) to E(–2, –5)
R(3, 2) and S(–3, –1)
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
x
8
10
x