2. What is Geometry?
•It is the branch of mathematics that deals with
lines, points, curves, angles, surfaces, and solids.
3. The following key terms are important to know when discussing angles.
Point A specific location on an object or a
(•) specific position in space.
Line A connected set of points that extends
without end in two directions.
Line Segment A piece of a line, like a jump rope.
Ray Part of a line that extends indefinitely in
4. Term Definition
Parallel Lines Lines that are always the same distance They
will never intersect.
Lines that form a right angle when they
Intersecting Lines Lines that cross, or that will cross. The point at
which they cross is called the vertex.
Transversal Lines Lines that intersect a set of parallel lines.
5. What are angles?
•An angle measures the amount of a turn.
•As the Angle Increases, the Name Changes.
Mr. Smiles fell
at an angle of
90⁰. He fell at
a right angle.
Pictures from clipart
6. Type of Angle Description
Acute An angle less than 90⁰
Right An angle that is exactly 90⁰
Obtuse An angle that is greater than 90⁰
Straight An angle that is exactly 180⁰
Reflex An angle that is greater than 180⁰
20. Parts of an Angle
•The two straight sides
are called rays.
• The point at which
the two rays meet is
called the vertex.
•The angle is the
amount of a turn
· Vertex between each ray.
21. Naming Angles
•There are two main ways to name angles:
1) Name an angle by the vertex.
A For example: B is the point at
C which both rays intersect.
2) Name an angle by all three
For example: A B C or
HINT: The vertex is always the
22. Guided practice
•Directions: Name and classify the following
angles. (Provide 3 ways to name each angle.)
C Acute Angle
Reflex Angle D EDC
4. Right Angle
F Obtuse Angle IJK
23. Supplementary Angles
The two angles below (140⁰ + 40⁰) are supplementary
angles, because their measurements add up to 180⁰.
NOTICE: When the two angles are put together, they
form a straight line.
29. Complementary vs Supplementary
How can you remember which is which? Easy! Think:
• "C" of Complementary stands for "Corner" (a Right
• "S" of Supplementary stands for "Straight" (180
degrees is a straight line)
<AFB and <BFC are complementary angles. If m<AFB = 50 ⁰, which
expression could be used to find the measure of <BFC?
1. 180⁰ - 50 ⁰
2. 90 ⁰ + 50 ⁰
3. 180 / 50 ⁰
4. 90 ⁰ (50 ⁰ )
35. Guided Practice
1. The train crosses Sesame Street and Big Bird Avenue at
an angle of 60⁰. What is the measure of the
HINT: a line
equals 180⁰. 180⁰ - 60⁰ = 120⁰ Big Bird Ave.
36. 2. Jo Jo is building a fence. In order to make it stronger,
she will need to use a brace from one side to the ground.
If the brace makes a 45⁰ angle with the fence what is the
measure of the supplementary angle?
38. Angles Formed by A Transversal
A transversal line is a line that cuts
through a set of parallel lines.
This reads as Line AB is
parallel to Line CD.
As the transversal cuts through, it
forms both Corresponding and
Corresponding angles have equal
measurements, and vertical angles
have equal measurements. Transversal line
39. Corresponding Angles
The angles that occupy the
same relative position at each
The following angles are
3 & 7
1 & 5
2 & 6
Example: If 3 is 130⁰,
4 & 8 then 7 is also 130⁰.
Therefore, the angles will have
the same measurement.
40. Vertical Angles
Vertical angles are angles that are
opposite from each other.
For example: 2& 4 are
vertical, because they are
2 1 diagonal from each other.
Therefore, if 2 equals
C 6 5 D 50⁰, then 4 is also 50⁰.
41. Guided Practice Identify the vertical angles.
Directions: Fill in the missing angles if angle
1 equals 75⁰ 1 4
A 1 2 B
C D Identify the corresponding angles.
F 2 6
42. 1 2 3 4
5 6 7 8
If the lines are parallel and m<2 is 45⁰ in the figure above, what is
the measure of <3?
1. 30 ⁰
2. 45 ⁰
3. 90 ⁰
4. 135 ⁰
5. 180 ⁰
43. Vertical Angles vs. Corresponding
*Vertical angles are always equal. However, you can not assume you have
corresponding angles unless dealing with a transversal.
Why do I need to know about triangles?
The GED Test will ask testers to identify missing angles. In order to
answer those questions, a person must have an understanding of
triangles and their characteristics.
A triangle has three sides and three angles
The three angles always add up to 180°
a + b + c = 180⁰
45. Equilateral, Isosceles and Scalene
There are three special names given to triangles that tell
how many sides are equal.
Three equal sides
Three equal angles, always 60°
Two equal sides
Two equal angles
No equal sides
No equal angles