Bellwork

Write 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.

42 42 '

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 ? Can you assume that ? Can you assume that is a straight

angle? Name a point between R and T.

JR KT

R T RST

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.)