Geometry 6-5 Conditions for Rhombuses, Rectangles, and Squares

by Matthew Richardson

| 29 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

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1

10 pts

Solve It! Which vertices form a square? Select all that apply.

AFEO

BCDG

GDHO

GJFL

2

10 pts

Problem 1 Got It? A parallelogram has angle measures of 20, 160, 20, and 160. Can it be a rhombus, a rectangle, or a square?

Rhombus

Rectangle

Square

3

10 pts

Problem 1 Got It? Explain your response on the previous item.

4

10 pts

Problem 1 Got It? Reasoning: Suppose the diagonals of a quadrilateral bisect each other. Can you conclude that it is a rhombus, a rectangle, or a square?

Rhombus

Rectangle

Square

The quadrilateral is none of these.

There is not enough information to make a conclusion.

5

10 pts

Problem 1 Got It? Explain your response on the previous item.

6

6

10 pts

Problem 2 Got It?

A

B

C

D

7

7

10 pts

Problem 3 Got It? Can you adapt the method in Problem 3 slightly to stake off a square play area? Explain.

8

9

10

11

8

10 pts

Based on the given information, what are the possible classifications for the parallelogram?

Select all that apply.

Rhombus

Rectangle

Square

None of these

9

10 pts

Explain your response to the previous item.

10

10 pts

Based on the given information, what are the possible classifications of the parallelogram?

Select all that apply.

Rhombus

Rectangle

Square

None of these

11

10 pts

Explain your response to the previous item.

12

12

10 pts

A

B

C

D

13

13

10 pts

A

B

C

D

14

10 pts

Identify the special parallelograms that have each property.

- Rhombuses
- Rectangles
- Squares

- Diagonals are perpendicular
- Diagonals are congruent
- Diagonals are angle bisectors
- Diagonals bisect each other
- Diagonals are perpendicular bisectors of each other

15

10 pts

Error Analysis: Your friend says, "A parallelogram with perpendicular diagonals is a rectangle." What is your friend's error? Explain.

16

10 pts

Reasoning: Complete the following steps on the canvas.

1. Draw a circle and two of its diameters.

2. Connect the endpoints of the diameters to form a quadrilateral.

17

10 pts

Reasoning: Which types of quadrilaterals are possible in the previous item? Select all that apply.

Rhombuses

Rectangles

Squares

None of these

18

10 pts

Review Lesson 6-4: Use the parallelograms in the diagrams above to match the measures with their angles.

(Tip: You may need to use the down arrow key to drag items to the lowest angle measures.)

- 58
- 26
- 90
- 57
- 128
- 66

- ∠A
- ∠B
- ∠C
- ∠D
- ∠E
- ∠F
- ∠G
- ∠H
- ∠I

19

10 pts

Review Lesson 2-3: Write the two conditionals as a biconditional.

If a parallelogram is a rhombus, then its diagonals are perpendicular.

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

20

10 pts

Review Lesson 2-3: Write the two conditionals as a biconditional.

If a parallelogram is a rectangle, then its diagonals are congruent.

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Review Lesson 1-3

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24

21

10 pts

Find the value of a.

Enter only a number.

22

10 pts

Find the value of b.

Enter only a number.

23

10 pts

Find the value of m.

Enter only a number.

24

10 pts

Find the value of n.

Enter only a number.

25

10 pts

Vocabulary Review: Cross out the figure that is NOT a quadrilateral.

26

10 pts

Use Your Vocabulary: Which polygon has no diagonal ?

triangle

quadrilateral

pentagon

hexagon

27

10 pts

Use Your Vocabulary: Which polygon has two diagonals ?

triangle

quadrilateral

pentagon

hexagon

28

10 pts

Use Your Vocabulary: Draw the diagonals from one vertex in each figure.

29

10 pts

Reflection: Math Success

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