Properties of a parallelogram Lesson Plan Properties of a parallelogram
Topic: Properties of a parallelogram
Grade Level: 10th
AIM: What are the properties of a parallelogram?
OBJECTIVES: By the end of the lesson, the students should be able to 1.
Define parallelogram.
2.
State th the fol folllowin wing pr proper perties of of a parallelogram:
a. opposite sides of a parallelogram are congruent b. opposite angles of a parallelogram are congruent c. consecutive angles of a parallelogram are supplementary d . the diagonals of a parallelogram bisect each other 3.
Prov Provee tha thatt a diag diagon onal al divi divide dess a para parall llel elog ogra ram m int into o two two cong congru ruen entt tri trian angl gles es..
4.
Appl Apply y the the prop proper erti ties es of a par paral alle lelo logr gram am in nume numeri rica call and and alg algeb ebra raic ic prob proble lems ms..
PRIOR KNOWLEDGE: •
Knowledge of parallel lines and of the angles formed when two parallel p arallel lines are cut
by a transversal. •
Past learned method of proving triangles congruent – ASA
MATERIALS/EQUIPMENT: - Proj Projec ecto tor, r, - Transp Transpare arenci ncies, es, - laptop laptop computer with Geometer’s Geometer’s Sketchpad Sketchpad (GSP) (GSP) Software Software
MOTIVATION: Picture will be presented as a power point slide.
- The picture picture shows the the tiling of a floor. floor. What geometr geometric ic figures were used to tile the floor?
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Properties of a parallelogram Lesson Plan DEVELOPMENT:
I. Homework Review
Students will present and explain their work to the class using transparencies.
II. Introduce unit – quadrilaterals
1. Define quadrilateral 2. Review the parts of a quadrilateral using a GSP presentation. -
Consecutive/adjacent vertices
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Consecutive/adjacent sides
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Opposite sides
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Consecutive angles
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Opposite angles
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Diagonal(s)
III. Explore the properties of a parallelogram
Use a GSP presentation to explore the properties of the parallelogram. Start by constructing a parallelogram and then measure the angles, the sides, and the diagonals. From observation of the presentation the class will learn the following properties of a parallelogram: opposite sides are congruent, opposite angles are congruent, consecutive angles are supplementary, diagonals bisect each other. [An example of the diagram that will be constructed is included at the end of the lesson plan.]
Show, using GSP, how each diagonal divides the parallelogram into two triangles. Ask students to explain why those triangles are congruent.
Pivotal Questions - Why are consecutive angles of a parallelogram supplementary? - Why are the triangles formed by each diagonal congruent?
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Properties of a parallelogram Lesson Plan IV. Example Problems – Applying the properties of a parallelogram to algebraic problems.
1. by
The degree measures of two opposite angles of a parallelogram are represented 3x + 40 and x + 70.
a. Find the value of x.
b. Find the degree measure of one of the angles. 2.
In parallelogram ABCD, the degree measure of angle
D
A is represented by 2 x and the degree measure of B represented 2 x + 60. Find the degree measure of angle A and the
by
C
B
degree measure of angle B.
Ex. 2 & 3
3.
In parallelogram ABCD, AB = 4x + 20 and CD = 6x – 10. Find AB and CD.
4.
If DE = 4y + 1 and EB = 5y – 1, find DB.
D
C E
A
B
Ex. 4–6
V. Practice problems – Applying the properties of a parallelogram to algebraic problems.
1. If m∠DAB = 4y - 60 and m
∠DCB = 30 - y,
find the degree measures of the angles of the parallelogram.
2. If AB = 4x + y, BC = y + 4, CD = 3x + 6, DA = 2x + y, find the lengths of the sides of the parallelogram.
ASSESSMENT: -
Questions
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Answers
-
comments
-
practice problems
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presentations
SUMMARY: 1. Using complete sentences, explain what are the properties of a parallelogram?
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Properties of a parallelogram Lesson Plan HOMEWORK:
B
1.
E
Given:
D
ABC is scalene, with altitudes AE and CD.
Prove: AE ≅ CD. C
A
2.
If DA ≅ CB and
∠ DAB ≅ ∠CBA,
D
prove that
AOB is isos celes.
C O
A
3.
Find the degree measures of the other three angles of a parallelogram if one angle measures: 60
4.
In ABCD, ∠A measures degree measure of ∠A.
5.
In ABCD, m ∠ABC = 3 x - 12 an m ∠CDA = m∠BCD, m∠DAB.
6.
In
7.
In ABCD, which is always true? (1) AB = AD (2) AB = DC
ABCD, AB = 7
D
x
x
egrees an
∠B measures
x
2 x - 30
egr ees . F n t e
+ 40. F n m∠ABC, m∠CDA,
- 4 and CD = 2 x + 21. Find AB and CD.
(3) AB AD
(4)
∠A ≅ ∠B
C E
A
B
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Properties of a parallelogram Lesson Plan Example of a parallelogram that the two students will be construct in class with GSP.
Sides’ lengths m AB = 14.7 cm
Angles’ measures
Bisected diagonals’ measures
m
BAC = 54.7
AE = 10.4 cm
m AC = 8.4 cm
m
ACD = 125.3
ED = 10.4 cm
m CD = 14.7 cm
m
CDB = 54.7
CE = 6.0 cm
m DB = 8.4 cm
m
DBA = 125.3
EB = 6.0 cm
C
D
E
A
B
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