Heather Leo

Summarizing Properties of Quadrilaterals Lesson

This lesson will summarize properties of quadrilaterals. It is intended to be used at the end of a

unit on quadrilaterals. It is intended for a junior high or high school math class.

Length of the Lesson:

(3) 40 minute class periods

Prerequisites:

Students must know the properties of parallelograms.

Students should be able to name some of the properties associated with different

quadrilaterals.

Students must be able to use Geometer’s Sketchpad (GSP).

Objectives:

By the end of the lesson, students will be able to:

understand the characteristics and properties of quadrilaterals.

apply the characteristics and properties of quadrilaterals.

Rationale for Specific Mediums:

Geometer’s Sketchpad

o Students can explore the different characteristics and properties of quadrilaterals.

o Students must design the template for understanding quadrilaterals furthering their

understanding of the activity.

Learning Activities, Sequence, and Procedure:

Day 1

Review of concepts needed for Summarizing Properties of Quadrilaterals ~ 10 minutes

1) Students respond to the review questions on the Warm-up: Summarizing Properties of

Quadrilaterals Worksheet.

2) As a class, students and teacher share and discuss question responses.

Geometer’s Sketchpad Summarizing Properties of Quadrilaterals Activity ~ 30 minutes

1) Students are each given a laptop and the Activity worksheet and instructed to open Geometer’s

Sketchpad.

2) Teacher displays the Geometer’s Sketchpad completed application on the screen so students

can use it to guide them when setting up the activity. (see GSP screenshot)

3) Students conduct the Summarizing Properties of Quadrilaterals GSP activity and complete the

table and questions.

4) Teacher will monitor activity, intervene and provide feedback as needed.

Homework

1) Students will finish questions 2 - 5 from the Summarizing Properties of Quadrilaterals GSP

activity worksheet if they did not complete them in class.

Day 2

Review of the Summarizing Properties of Quadrilaterals GSP Activity ~ 15 minutes

1) Teacher and students will review and discuss questions 1 – 5 from the GSP Activity worksheet.

The table from Question 1 will be displayed on the board.

Group Activity for Summarizing Properties of Quadrilaterals ~ 25 minutes

1) Students will be divided into groups of 3 and will do the Group Activity for Summarizing

Properties of Quadrilaterals. Students should use the information from the GSP activity to

complete the group activity.

2) Teacher will monitor discussions and provide feedback and corrections when needed.

Homework

1) Students will study for a quiz on the Properties of Quadrilaterals.

Day 3

Review of the Properties of Quadrilaterals ~ 5 minutes

1) Students will do the Quadrilateral Review worksheet.

2) Teacher and students will discuss the answers to the worksheet.

Preparation for Assessment ~ 10 minutes

1) Teacher will write the names of the quadrilaterals on the board.

2) Students will be asked to name the properties of the quadrilaterals and teacher will record on

the board. Teacher will be sure that all properties are covered.

Assessment: Summarizing Properties of Quadrilaterals Quiz ~25 minutes

1) Students will do Summarizing Properties of Quadrilaterals Quiz independently as a quiz grade.

2) Teacher will correct and assess the quiz using the provided rubric.

Materials Needed:

Geometer’s Sketchpad (see screenshot at the end of lesson)

Warm-up: Summarizing Properties of Quadrilaterals worksheet (see end of lesson)

Summarizing Properties of Quadrilaterals Geometer’s Sketchpad Activity worksheet (see end of

lesson)

Group Activity: Summarizing Properties of Quadrilaterals worksheet (see end of lesson)

Quadrilateral Review worksheet(see end of lesson)

Quiz: Summarizing Properties of Quadrilaterals and Rubric worksheet (see end of lesson)

Feedback and Assessment:

Teacher will visit students during the Summarizing Properties of Quadrilaterals GSP activity to

monitor activity, intervene and provide feedback as needed.

Teacher will assess student understanding of the properties of quadrilaterals while reviewing

the Summarizing Properties of Quadrilaterals GSP activity.

Teacher will visit groups during the Group Activity and monitor, intervene, and provide

corrections as needed.

Teacher will assess student understanding of the properties of quadrilaterals while preparing for

the assessment on day 3.

Formal Assessment

o Teacher will collect and evaluate Summarizing Properties of Quadrilaterals Quiz using

the rubric.

o Teacher will determine if additional instruction is required after reviewing the quiz.

Teacher will critique the lesson based on the feedback from the students during the activity.

Any revisions to the activities will be noted to improve upon the lesson.

Warm-up: Summarizing Properties of Quadrilaterals Name:___________________________

_____ 1. A rhombus is a quadrilateral.

_____ 2. If a quadrilateral is a square then it is also a rectangle.

_____ 3. If a quadrilateral is a trapezoid then it is also a parallelogram.

_____ 4. If a quadrilateral is a rectangle then it is also a square.

_____ 5. If a quadrilateral is a rhombus then it is also a square.

_____ 6. If a quadrilateral is a parallelogram then it is also a rhombus.

_____ 7. If a quadrilateral is a square then it is also a parallelogram.

_____ 8. An isosceles trapezoid is a parallelogram.

_____ 9. A rectangle is an isosceles trapezoid.

_____ 10. A quadrilateral with four congruent sides is a square.

_____ 11. A quadrilateral with four right angles is a rectangle.

_____ 12. A trapezoid has two pairs of parallel sides.

_____ 13. A rectangle has congruent opposite sides.

_____ 14. A parallelogram has one pair of parallel sides.

_____ 15. A parallelogram always has four congruent sides.

_____ 16. A kite has perpendicular diagonals.

Warm-up: Summarizing Properties of Quadrilaterals Name:_Answer Key________________

TRUE_____ 1. A rhombus is a quadrilateral.

TRUE_____ 2. If a quadrilateral is a square then it is also a rectangle.

FALSE_____ 3. If a quadrilateral is a trapezoid then it is also a parallelogram.

FALSE_____ 4. If a quadrilateral is a rectangle then it is also a square.

FALSE_____ 5. If a quadrilateral is a rhombus then it is also a square.

FALSE_____ 6. If a quadrilateral is a parallelogram then it is also a rhombus.

TRUE_____ 7. If a quadrilateral is a square then it is also a parallelogram.

FALSE_____ 8. An isosceles trapezoid is a parallelogram.

FALSE_____ 9. A rectangle is an isosceles trapezoid.

FALSE_____ 10. A quadrilateral with four congruent sides is a square.

TRUE_____ 11. A quadrilateral with four right angles is a rectangle.

FALSE_____ 12. A trapezoid has two pairs of parallel sides.

TRUE_____ 13. A rectangle has congruent opposite sides.

FALSE_____ 14. A parallelogram has one pair of parallel sides.

FALSE_____ 15. A parallelogram always has four congruent sides.

TRUE_____ 16. A kite has perpendicular diagonals.

Geometer’s Sketchpad Activity Screenshot

Group Activity: Summarizing Properties of Quadrilaterals Name:__________________________

Look at each set of figures. Which shape(s) would you exclude from the rest? You must justify why you believe your

answer is correct. Assume all figures are not drawn to scale so look at the markings on the figure to help you. Be as

detailed and specific as possible.

Set #1

A

Set #2

A

B

B

C

C

D

D

E

E

Set #3 - Assume all are parallelograms

B D E

C

A

Group Activity: Summarizing Properties of Quadrilaterals Answer Key

Set 1: Shape B should be excluded since it is not necessarily a parallelogram. Shape B could also be a trapezoid.

Set 2: Shape E should be excluded since it is not necessarily a rectangle.

Set 3: Shape C should be excluded since it is not necessarily a square.

Quiz: Summarizing Properties of Quadrilaterals Name:___________________________

Answer each of the questions below. Each of the problems (1a – 1e and 2) are worth 3 points and will

be evaluated using the rubric provided.

1. Draw and label as many different quadrilaterals that you can with the following properties:

a. Congruent diagonals

b. Perpendicular diagonals

c. Exactly one pair of congruent sides

d. At least one pair of opposite angles congruent

e. At most one pair or opposite congruent sides

2. You have decided to make a rectangular picture frame with side lengths 20 in by 16 in. You

hope that your frame is in the shape of a rectangle but you don’t have any way to measure the

angles. Based on the properties of rectangles, what other measurement(s) could you find in

order to be sure your frame is rectangle? Explain your answer

Evaluation Rubric

Summarizing Properties of Quadrilaterals Evaluation Rubric

Problem 1 (a – e) (Objective 1)

3 points The response contains all of the quadrilaterals that contain the property.

The response shows a correct drawing and label for each of the quadrilaterals.

2 points The response contains all of the quadrilaterals that contain the property.

The response is missing drawings or labels for the quadrilaterals or the label and drawing of a quadrilateral are incorrect.

1 point The response is missing quadrilaterals or contains quadrilaterals that do not contain the property.

The response shows a correct drawing and label for each of the quadrilaterals.

0 points The response is missing quadrilaterals or contains quadrilaterals that do not contain the property.

The response is missing drawings or labels for the quadrilaterals or the label and drawing of a quadrilateral are incorrect.

Problem 2 (Objective 2)

3 points The response shows complete understanding of the properties of rectangles.

The response contains a clear explanation.

2 points The response shows complete understanding of the properties of rectangles.

The explanation is not clear or contains minor errors.

1 point The response shows limited understanding of the properties of rectangles.

The explanation is clear but contains errors or an explanation is not given.

0 points The response shows insufficient understanding of the properties of rectangles.

There is no explanation or the explanation is not clear.

Quiz: Summarizing Properties of Quadrilaterals Name:__Answer Key_______________

1. Draw and label as many different quadrilaterals that you can with the following properties:

a. Congruent diagonals

Rectangle, Square, Isosceles Trapezoid, some Kites

b. Perpendicular diagonals

Rhombus, Square, Kite

c. Exactly one pair of congruent sides

Isosceles Trapezoid

d. At least one pair of opposite angles congruent

Kite, Rhombus, Parallelogram, Square, Rectangle

e. At most one pair or opposite congruent sides

Trapezoid, Isosceles Trapezoid

2. You have decided to make a rectangular picture frame with side lengths 20 in by 16 in. You

hope that your frame is in the shape of a rectangle but you don’t have any way to measure the

angles. Based on the properties of rectangles, what other measurement(s) could you find in

order to be sure your frame is rectangle? Explain your answer.

The diagonals would have to be congruent.