geometry quadrilaterals -1-...

Geometry – Quadrilaterals -1- NJCTL.org

Name______________________________ Date ____________________________ Lab: Quadrilaterals in the Coordinate Plane Objective In this lab you will investigate a specific quadrilateral. In your assigned groups you will look for special properties, such as parallel sides, congruent sides/diagonals, right angles and congruent diagonals. You will use algebraic tools such as the distance formula and slope formula to find these special properties. After analyzing the properties of your figure you will then classify your quadrilateral and explain. Your group will be graded on:

Your ability to work with each other and communicate through your individual roles.

The neatness and organization of your work.

The completeness and accuracy of your answers.

Your understanding and explanations of quadrilateral classification. Please see attached for Rubric. Roles: Time Keeper

You have 30 minutes to complete this activity.

Keep your group members informed of the time left, otherwise you will lose points. Recorder

You are responsible for neatly writing the group member names on the blank paper provided.

Also, you are to record all final calculations for the activity. Manager

You are to ensure that all team members stay on task and contribute to the group.

You are responsible for the completion of the activity. Checker

You are to double-check all calculations for accuracy.

You should also make sure that your group completes all necessary parts of the activity.


Grading Rubric


Quadrilaterals in the Coordinate Plane (A) Group: ___________ Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-2,2) O(1,6) H(6,6) S(3,2)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


W(-2,2) O(1,6) H(6,6) S(3,2) Part 2:

Slope Length

Sides

1.

2.

3.

4.

Diagonals

1.

2.

________________________________________________________________________________________ Part 3: Explain mathematically how you know that the quadrilateral is or is not each of the following types of quadrilaterals.

a. Parallelogram b. Rectangle c. Rhombus d. Square


Quadrilaterals in the Coordinate Plane (B) Group: ___________ Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(1,-4) B(3,-1) L(7,-1) S(5,-4)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: W(1,-4) B(3,-1) L(7,-1) S(5,-4)

Slope Length

Sides

1.

2.

3.

4.

Diagonals

1.

2.




Quadrilaterals in the Coordinate Plane (C) Group: ___________ Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: D(1,3) Q(2,5) R(8,2) P(7,0)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: D(1,3) Q(2,5) R(8,2) P(7,0)

Slope Length

Sides

1.

2.

3.

4.

Diagonals

1.

2.




Quadrilaterals in the Coordinate Plane (D) Group: ___________ Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: A(4,0) B(7,4) C(3,7) D(0,3)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: A(4,0) B(7,4) C(3,7) D(0,3)

Slope Length

Sides

1.

2.

3.

4.

Diagonals

1.

2.




Quadrilaterals in the Coordinate Plane (E) Group: ___________ Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-3,-1) B(-2,2) G(3,2) O(2,-1)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: W(-3,-1) B(-2,2) G(3,2) O(2,-1)

Slope Length

Sides

1.

2.

3.

4.

Diagonals

1.

2.




Quadrilaterals in the Coordinate Plane (F) Group: ___________ Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: K(7,1) I(7,5) N(0,5) D(0,1)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: K(7,1) I(7,5) N(0,5) D(0,1)

Slope Length

Sides

1.

2.

3.

4.

Diagonals

1.

2.




Quadrilaterals in the Coordinate Plane (A) Group: ANSWER KEY Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-2,2) O(1,6) H(6,6) S(3,2)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


W(-2,2) O(1,6) H(6,6) S(3,2)

Part 2:

Slope Length

Sides

1. 𝑊𝑂̅̅ ̅̅ ̅ 4

3 5

2. 𝑂𝐻̅̅ ̅̅ 0 5

3. 𝐻𝑆̅̅ ̅̅ 4

3 5

4. 𝑊𝑆̅̅̅̅̅ 0 5

Diagonals

1. 𝑂𝑆̅̅̅̅ -2 √20 = 2√5 ≈ 4.47

2. 𝑊𝐻̅̅ ̅̅ ̅ 1

2 √80 = 4√5 ≈ 8.94



Quadrilateral WOSH is a rhombus because both pairs of opposite sides are parallel, all of the sides have a length of 5, and the diagonals are perpendicular. Since WOSH is a rhombus, it is also considered to be a parallelogram.


Quadrilaterals in the Coordinate Plane (B) Group: ANSWER KEY Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(1,-4) B(3,-1) L(7,-1) S(5,-4)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: W(1,-4) B(3,-1) L(7,-1) S(5,-4)

Slope Length

Sides

1. 𝑊𝐵̅̅ ̅̅ ̅

3

2 √13 ≈ 3.61

2. 𝐵𝐿̅̅̅̅ 0 4

3. 𝐿𝑆̅̅ ̅

3

2 √13 ≈ 3.61

4. 𝑊𝑆̅̅̅̅̅ 0 4

Diagonals

1. 𝐵𝑆̅̅̅̅ −

3

2 √13 ≈ 3.61

2. 𝑊𝐿̅̅̅̅̅

1

2 √45 = 3√5 ≈ 6.71



Quadrilateral WBLS is a parallelogram because both pairs of opposite sides are parallel and congruent. There are no perpendicular lines (so no right angles), and the sides are not all congruent. Therefore, parallelogram WBLS is not a rhombus, rectangle, or a square.


Quadrilaterals in the Coordinate Plane (C) Group: ANSWER KEY Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: D(1,3) Q(2,5) R(8,2) P(7,0)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: D(1,3) Q(2,5) R(8,2) P(7,0)

Slope Length

Sides

1. 𝐷𝑄̅̅ ̅̅ 2 √5 ≈ 2.24

2. 𝑄𝑅̅̅ ̅̅ −

1

2 √45 = 3√5 ≈ 6.71

3. 𝑅𝑃̅̅ ̅̅ 2 √5 ≈ 2.24

4. 𝐷𝑃̅̅ ̅̅ −

1

2 √45 = 3√5 ≈ 6.71

Diagonals

1. 𝐷𝑅̅̅ ̅̅ −

1

7 √50 = 5√2 ≈ 7.07

2. 𝑄𝑃̅̅ ̅̅ –1 √50 = 5√2 ≈ 7.07



Quadrilateral DQRP is a rectangle because both pairs of opposite sides are parallel and congruent. Also, the adjacent sides are perpendicular to each other, which form 4 right angles. Also, the diagonals are congruent. Therefore, quadrilateral DQRP is a rectangle. Since DQRP is a rectangle, it is also considered to be a parallelogram.


Quadrilaterals in the Coordinate Plane (D) Group: ANSWER KEY Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: A(4,0) B(7,4) C(3,7) D(0,3)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2:

A(4,0) B(7,4) C(3,7) D(0,3)

Slope Length

Sides

1. 𝐴𝐵̅̅ ̅̅

4

3 5

2. 𝐵𝐶̅̅ ̅̅ −

3

4 5

3. 𝐶𝐷̅̅ ̅̅

4

3 5

4. 𝐴𝐷̅̅ ̅̅ −

3

4 5

Diagonals

1. 𝐷𝐵̅̅ ̅̅

1

7 √50 = 5√2 ≈ 7.07

2. 𝐶𝐴̅̅ ̅̅ –7 √50 = 5√2 ≈ 7.07



Quadrilateral ABCD is a square because it has the qualities of all of the quadrilaterals listed above. Both pairs of opposite sides are parallel, so it’s considered to be a parallelogram. Adjacent sides are perpendicular and the diagonals are congruent, so it’s considered to be a rectangle. All 4 sides are congruent, and the diagonals are perpendicular, so it is also considered a rhombus. Since it has the qualities of both a rhombus and a rectangle, quadrilateral ABCD is a square.


Quadrilaterals in the Coordinate Plane (E) Group: ANSWER KEY Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: W(-3,-1) B(-2,2) G(3,2) O(2,-1)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2:

W(-3,-1) B(-2,2) G(3,2) O(2,-1)

Slope Length

Sides

1. 𝑊𝐵̅̅ ̅̅ ̅ 3 √10 ≈ 3.16

2. 𝐵𝐺̅̅ ̅̅ 0 5

3. 𝐺𝑂̅̅ ̅̅ 3 √10 ≈ 3.16

4. 𝑊𝑂̅̅ ̅̅ ̅ 0 5

Diagonals

1. 𝐵𝐶̅̅ ̅̅ −

3

4 5

2. 𝑊𝐺̅̅ ̅̅ ̅

1

2 √45 = 3√5 ≈ 6.71



Quadrilateral WBLS is a parallelogram because both pairs of opposite sides are parallel and congruent. There are no perpendicular lines (so no right angles), and the sides are not all congruent. Therefore, parallelogram WBLS is not a rhombus, rectangle, or a square.


Quadrilaterals in the Coordinate Plane (F) Group: ANSWER KEY Directions: Below you are given a quadrilateral. You will be analyzing the sides and diagonals of the quadrilateral. Plot your points on the graph below and label them. Connect all vertices of the quadrilateral and draw the two diagonals. Calculate the slope of each side and of the two diagonals. Show your work on the back of this paper. Calculate the length of each side and of the two diagonals. Show your work on the back of this paper. Part 1: K(7,1) I(7,5) N(0,5) D(0,1)

Time Keeper: ___________________________

Recorder: ______________________________

Manager: ______________________________

Checker: _______________________________


Part 2: K(7,1) I(7,5) N(0,5) D(0,1)

Slope Length

Sides

1. 𝑁𝐷̅̅ ̅̅ undefined 4

2. 𝑁𝐼̅̅̅̅ 0 7

3. 𝐼𝐾̅̅ ̅ undefined 4

4. 𝐾𝐷̅̅ ̅̅ 0 7

Diagonals

1. 𝑁𝐾̅̅̅̅̅ −

4

7 √65 ≈ 8.06

2. 𝐷𝐼̅̅ ̅

4

7 √65 ≈ 8.06



Quadrilateral NIKD is a rectangle because both pairs of opposite sides are parallel and congruent. Also, the adjacent sides are perpendicular to each other, which form 4 right angles. Also, the diagonals are congruent. Therefore, quadrilateral NIKD is a rectangle. Since NIKD is a rectangle, it is also considered to be a parallelogram.

geometry quadrilaterals -1-...

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