Download University of West Alabama COE 5E Lesson Plan

University of West Alabama
COE
5E Lesson Plan
Teacher: Rebecca Mitchell
Date: January 6
Subject area/course/grade level: Geometry/course/10th
Materials: Holt Geometry Text Book, Proof: Perpendicular Bisector Theorem Video, Computer with internet Access
Standards: Prove theorems about lines and angles. Theorems include vertical angles are congruent; when a transversal
crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; and points on a
perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. [G-CO9]
Objectives: The students will be able to prove and apply theorems about perpendicular bisectors. The students will be able
to prove and apply theorems about angle bisectors. The students will be able to identify equidistant and locus points.
Differentiation Strategies:
ENGAGEMENT:
I will show the students a map of the city on which the school is located. I will have two marks previously marked for
example the school can be marked and the local grocery store. I will have the students pick places on the map that
they feel are the same distance from both locations. After the students have found several different places, I will show
the students that all these places lie near the perpendicular bisector of the segment joining the two original locations. I
will then explain to the students that they will be learning properties like this in this lesson.
EXPLORATION:
Think Pair Share (20 min)
Students will work in their groups on Investigation 1(attached). I will be responsible for
passing out rulers and protractor. The teacher should monitor the students closely to make
sure they stay on track. While they are working in their groups the teacher should ask the
following questions:
What is a perpendicular bisector?
What will you use your ruler for?
What will you use your protractor for?
What are you trying to do in this investigation?
Does everyone in the group understand?
EXPLANATION:
The teacher will do an I-DO WE-DO YOU-DO Strategy to explain the concept to the students. It is
attached.
ELABORATION:
Students will create their own presentation on Prezi.com. The students will continue to work
in the groups of four that they are in. They will need computers with internet access. Refer
to Investigation 2. While they are working in groups the I will ask the following questions:
What is a perpendicular bisector?
What is an angle bisector?
How will you organize your prezi?
How will you use the graphic organizer to help?
What research are you doing on the internet to help you?
Why shouldn’t you just copy and paste?
What are you trying to do in this investigation?
Does everyone in the group understand?
EVALUATION:
The evaluation will be done throughout with the constant questioning. I will also asses when the students do their
presentations of their prezi.
Investigation 1
Perpendicular and Angle Bisectors
Use a ruler and a protractor to investigate the properties of perpendicular bisectors.
l
1. Draw a long segment on a sheet of paper and label it AB.
2. Find the midpoint of the segment by using a ruler. Label the midpoint P
A
P
B
3. Take a protractor and draw a line through P that is perpendicular (forms a 90 degree angle) to
line AB. Label that line l .
4. Draw any point X on line l . Then measure the distance from X to A and then measure the
distance from X to B. What do you observe?
5. Now make three more points on l and measure the distance from each point to both endpoints.
What do you observe?
6. Make a conjecture by completing the following sentence: If a point is on the perpendicular
bisector of a segment, then ________.
Think and Discuss
7. How you can use your conjecture and the fact that line l is the perpendicular bisector of line AB
to classify triangle AXB.
EXPLANATION
During: I DO- WE DO- YOU DO (20 min)
The teacher will present the class with the first example:
A. (I-DO) Find the measure of YW, if XW = 7
YW = ?
YW =XW Perpendicular Bisector Thm.
YW = 7 Substitute 7 for XW.
X
W
Z
Y
B. (WE-DO) Find the measure of BC, if AB = 36, AC = 36, and DC = 16.
Since AB = AC and line l is perpendicular to BC, line l is the
perpendicular bisector of BC by the Converse of the Perpendicular
Bisector Theorem.
B
BC = 2DC
Definition of segment bisector
BC = 2(16) = 32
Substitute 16 for DC
D
A
C
C. (YOU-DO) Find the measure of PR, if PS = QS, PR = 2n + 9, and RQ =
7n – 18.
P
S
Q
PR = RQ
Perpendicular Bisector Thm.
2n + 7 = 7n – 18 Substitute the given values.
7 = 5n – 18
Subtract 2n from both sides.
25 = 5n
Add 18 to both sides.
5=n
Divide both sides by S.
So PR = 2(5) + 7 = 17
R