2. Line segments with equal measures are ______. - Saratoga High ...

Warm up 1.4
Fill in the blanks.
1. The endpoint of RQ is ________.
2. Line segments with equal measures are ________.
3. A rule of geometry that is accepted without proof is
a _____________.
4. A pair of opposite rays form a ________.
State the distance between the following coordinates
on a number line.
5. -3 and -8 6. 4 and -1
7. -2.2 and 2.2 8. 12 and -1.5
9. Find the length of OQ if MQ = 30, MN = 5,
MN = NO, and OP = PQ.
M N O P Q

Thursday Sept 17 th
Warm-up
HW Questions
Notes: 1.4 Angles
Measuring Activity
Notes: 1.5 Postulates & Theorems

Pg. 15 #5-18, 27-40
6. False 8. True 10. True 12. True
14. False 16. False 18. True
28. 30.
32. -7, 5, 8 34. X = 11
36. X = 7 38. Y = 7
40. Z = 5, GE = 5, EH = 6; no

1.4 Angles
angle - consists of two different rays that have the same
initial point.
vertex - the initial point of each ray that forms an angle.
EX
Name the angles in the figure.

_____________ angles have equal measures.
Two angles in a plane that have a common vertex and a
common side but no common interior points are called
__________ angles.
An angle ___________ is the ray that divides the angle into
two congruent adjacent angles.
P
Q
S
R

Measuring Angles

Classifying Angles:
Measure and Example
ACUTE
RIGHT
OBTUSE
STRAIGHT
Measuring Activity!.... worksheet

Ray PT is the angle bisector of

Ray BT bisects

There are things that you can assume in Geometry, and there are things
you can’t. Let figure them out.
List all the conclusion from the diagram on the
right.
A
D
All points shown are coplanar.
line AB, ray BD, and ray BE intersect at B.
A, B, and C are collinear
∠ABC is a straight angle.
D is in the interior of ∠ABE.
∠ABD and ∠DBE are adjacent angles.
B
C
E
(1) You can’t assume size or measurement. This means that you can’t
assume congruence and right angle.
(2) You can assume relative positions and collinearity.

1.5 Postulates & Theorems
Postulate 5
A line contains at least ____ points; a plane consists at least _____ points not all
in one line; space contains at least ______ points not all in one plane.
Postulate 6
Through any two points there is exactly _____ line.
Postulate 7
Through any three points there is ______ one plane, and through any three
noncollinear points there is __________ one plane.
Postulate 8
If two ______ are in a plane, then the line that contains the _____ is in that
plane.
Postulate 9
If two planes intersect, then their intersection is a _______.

Theorem 1-1
If two ______ intersect, then they intersect in exactly one _______.
Theorem 1-2
Through a line and a point not in the line there is exactly one _______.
Theorem 1-3
If two ______ intersect, then exactly one plane contains the _______.
Example
Classify each statement as true or false. Give the definition, postulate or
theorem that supports your conclusion.
1. A given triangle can lie in more than one plane.
False. Through a line and a point not in the line there is exactly 1 plane.
2. Any two points are collinear.
True. Through any 2 pts there is exactly 1 line.
3. Two planes can intersect in only one point.
False. If 2 planes intersect (int.), then their int. is a line.
4. Two lines can intersect in two points.
False. If 2 lines int., then they int. in exactly 1 pt.

Extra
Quick Quiz
Complete with always, sometimes, or never.
always
1. Two points _____________ line in exactly one line.
sometimes
2. Three points _____________ lie in exactly one line.
sometimes
3. Three points _____________ lie in exactly one plane.
never
4. Three collinear points _____________ lie in exactly one plane.
sometimes
5. Two planes _____________ intersect.
never
6. Two intersecting lines _____________ in exactly one point.
always
7. Two intersecting lines _____________ intersect in exactly one point.
sometimes
8. Two line _____________ intersect in exactly one point.
always
9. Two intersecting lines _____________ lie in exactly one plane.
10. A line and a point not on that line _____________ never lie in more than one plane.
11. A line _____________ never contains exactly one point.
12. When A and B are in a plane, line AB _____________
always
in that plane.

Monday
Homework
Tuesday/
Wednesday
Thursday/
Friday
9/14
Pg. 7 #1-10, 21 - 33
Written exercises
NOT Class Exs
9/15-16
Pg. 15 #5-18all,
27-40all
9/17-18
Pg. 21#1-22all,
#29-34all &
Pg. 25 #5-19 all