Download Angles Notes Aug. 24th

Pre-AP Geometry
Unit 1
Points, Lines, Planes Review and
Angles Lesson
Think on This, True of False.
1.
2.
3.
4.
5.
6.
PF ends at P.
Point S is on an infinite number of lines.
A plane has no thickness.
Planes have edges.
Two planes intersect in a line segment.
Two intersecting lines meet in exactly one
point.
7. Points have no size.
Points, Lines, and Planes
• Opposite Rays
▫ If C is between A and B, then CA and CB are
opposite rays.
▫ Together they make a line.
A
C
B
Lesson 1.4: Angles
Parts of an angle
• Sides of an angle are made up of rays
• The rays meet at a point called the vertex
vertex
sides
Naming an angle
• An angle can be named by the vertex, by the 3 points on the
angle: the side, the vertex and the other side, or a number
inside the angle.
G
1
H
I
The angle can be named ∠GHI, ∠IHG, ∠H, or ∠1
Classifying angles
• Acute angle: Angle measuring greater than 0°
and less than 90°.
• Obtuse angle: Angle measuring greater than 90°
and less than 180°
• Right angle: An angle measuring exactly 90°
• Straight angle: An angle measuring exactly 180°
Angle Vocabulary
• Congruent Angles
▫ Two angles with equal measures
• Adjacent angles
▫ Angles which share a vertex and a common side,
but no common interior points
• Angle bisector
▫ A ray which divides an angle into two congruent,
adjacent angles
Congruence symbols and drawing
conclusions
• Do not assume anything in geometry. Just
because two segments look equal does not mean
that they are.
Postulates
A point is defined by its location.
A line contains at least two points.
A plane contains at least three points not all in one line.
Space contains at least four points not all in one plane.
Postulates – Based on reasoning,
discussion and belief.
Through any two points there is exactly one line.
Through any three points there is at least one plane and
through any three non-collinear points there is exactly
one plane.
If two points are in a plane, then the line that contains
the point is in that plane.
If two planes intersect, then their intersection is a line.
Theorem – Truth considered based
on postulates
If two lines intersect, then they intersect in exactly one
point.
Theorem
Through a line and a point not in the line there is exactly
one plane.
Solo Time: Consider these. Answer true or
false then state why. You have 2 minutes.
•
Group Time:
Work through the problems on page 11 of the textbook.
Wrap-Up
Reflect on what we learned today.
Are there any questions, misconceptions still?
What do we need to be careful with when naming angles?