Transcript 1.3 Collinearity, Betweenness and Assumptions-

Bellwork

Write 4242 ' in degrees.
When you’re finished, confer with your
partner.
 Feel free to do a problem listed on the
board if you haven’t earned your chapter
points yet.

Example 4

Find the measure of the angle formed by
the hands of a clock at 2:30.
1.3 Collinearity,
Betweenness and
Assumptions
Students will be able to:
1. Recognize when points are collinear
or between two points.
2. Apply the triangle inequality
theorem.
3. Correctly interpret geometric
diagrams.
Collinear– (a definition)
Points that lie on the same line
 Any two points are collinear.
 Name three collinear points from the
diagram.

Betweenness (Defn)

C is between A and B if AC + CB = AB iff
(If and only if) A, B and C are collinear.
Example 1
Q is between P and R on a number line.
P = -8 and R = 4.
 What do we know about the coordinate of
Q?
 What do we know about the length of
PQ + QR?
Partner work
Take a bag of straws. Together make one
red, one green and one blue triangle.
What can you conclude about each
colored triangle?
Why do you think that is?
Triangle Inequality
Given that A, B and C are non-collinear
points, then three things are true:
Example 2

What are the restrictions on x given the triangle
below?

What theorem did you just use?
Make your notes look like this !
Assume
Can’t Assume
Assumptions—Yes, assume away!
pg. 19 shaded area
Straight lines and angles
 Collinearity
 Betweenness

Assumptions—No way, Jose!
Without markings!
 Congruent segments
 Right angles
 Congruent angles
 Relative sizes of segments or angles.
Example 3
Name three collinear points.
 Can you assume that JR  KT ?
 Can you assume that R  T ?
 Can you assume that RST is a straight
angle?
 Name a point between
R and T.

Ticket to Leave

Two of the sides of a triangle are 12 and
18. What are the possible lengths for the
third side of the triangle? Write as an
inequality statement.

What theorem did you use?
Homework
Pg. 21 #3 – 13,15
 Quiz Tomorrow sections 0.1-1.3
 Extra Credit: At what time between 2:00
and 3:00 are the tip of the minute hand,
the center of the clock face and the tip of
the hour hand collinear? (Turn in on a
separate sheet of paper from hwk.)
