geometry test squares, rhombi, kites, trapezoids a...

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Geometry Test Squares, Rhombi, Kites, Trapezoids Multiple Choice Identify the choice that best completes the statement or answers the question. Quadrilateral ABCD is a rectangle. A B C D G ____ 1. If and , find . a. 96 c. 24 b. 6 d. 48 ____ 2. If and , find . a. 48 c. 42 b. 1 d. 45 ____ 3. In rhombus YZAB, if 12, find . Y Z A B O a. 24 c. 6 b. 12 d. 12 2 ____ 4. In rhombus TUVW, if , find . T U V W O a. 56 c. 34 b. 68 d. 112 Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square. List all that apply.

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Geometry Test Squares, Rhombi, Kites, Trapezoids

Multiple Choice

Identify the choice that best completes the statement or answers the question.

Quadrilateral ABCD is a rectangle.

A B

CD

G

____ 1. If and , find .

a. 96 c. 24

b. –6 d. 48

____ 2. If and , find .

a. 48 c. 42

b. 1 d. 45

____ 3. In rhombus YZAB, if 12, find .

Y Z

AB

O

a. 24 c. 6

b. 12 d. 12 2

____ 4. In rhombus TUVW, if , find .

T U

VW

O

a. 56 c. 34

b. 68 d. 112

Given each set of vertices, determine whether parallelogram ABCD is a rhombus, a rectangle, or a square.

List all that apply.

____ 5. , , ,

a. square; rectangle; rhombus c. square

b. rhombus d. rectangle

____ 6. , , ,

a. rhombus c. square

b. square; rectangle; rhombus d. rectangle

____ 7. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.

J K

LM

A B31

34

a. 65 c. 28

b. 32.5 d. 3

____ 8. For trapezoid JKLM, A and B are midpoints of the legs. Find ML.

J K

LM

A B36

32

a. 4 c. 68

b. 34 d. 40

____ 9. For trapezoid JKLM, A and B are midpoints of the legs. Find AB.

J K

LM

A B

19

27

a. 23 c. 35

b. 8 d. 46

____ 10. For trapezoid ABCD, E and F are midpoints of the legs. Let be the median of ABFE.

Find GH.

A B

CD

E F

5

9

a. 7 c. 4

b. 8 d. 6

Position and label each quadrilateral on the coordinate plane.

____ 11. rectangle with side length b units and height d units

a.

(0, 0) ( 0)

(0, )( )

b,

b, dd

x

y

c.

(0, 0) ( 0)

(0, )( )

b + k,

b, dd

x

y

b.

(0, 0) ( 0)

(0, )( )

b,

b, bb

x

y

d.

(0, 0) ( , 0)

( ) ( )

d

c, b c + d, b

x

y

____ 12. square with side length b units

a.

(0, 0) ( 0)

(0, )( )

b,

b, dd

x

y

c.

(0, 0) ( 0)

(0, )( )

b + k,

b, dd

x

y

b.

(0, 0) ( 0)

(0, )( )

b,

b, bb

x

y

d.

(0, 0) ( , 0)

( ) ( )

d

c, b c + d, b

x

y

____ 13. trapezoid with height d units, bases b and units

a.

(0, 0) ( 0)

(0, )( )

b,

b, dd

x

y

c.

(0, 0) ( 0)

(0, )( )

b + k,

b, dd

x

y

b.

(0, 0) ( 0)

(0, )( )

b,

b, bb

x

y

d.

(0, 0) ( , 0)

( ) ( )

d

c, b c + d, b

x

y

____ 14. parallelogram with side length d units and height b units

a.

(0, 0) ( 0)

(0, )( )

b,

b, dd

x

y

c.

(0, 0) ( 0)

(0, )( )

b + k,

b, dd

x

y

b.

(0, 0) ( 0)

(0, )( )

b,

b, bb

x

y

d.

(0, 0) ( , 0)

( ) ( )

d

c, b c + d, b

x

y

____ 15. rectangle with side length 2k units and height 4k

a.

( 2 ) ( 2 )

( –2 ) ( –2 )

–k, k

–k, k k, k

k, k

x

y

c.

(–2 ) (2 )

(–2 ) (2 )

k, k

k, – k k, –k

k, k

x

y

b.

(–2 2 ) (2 2 )

(–2 –2 ) (2 –2 )

k, k

k, k k, k

k, k

x

y

d.

( ) ( )

( ) ( )

–k, k

–k, –k k, –k

k, k

x

y

____ 16. square with side length 4k units

a.

( 2 ) ( 2 )

( –2 ) ( –2 )

–k, k

–k, k k, k

k, k

x

y

c.

(–2 ) (2 )

(–2 ) (2 )

k, k

k, – k k, –k

k, k

x

y

b.

(–2 2 ) (2 2 )

(–2 –2 ) (2 –2 )

k, k

k, k k, k

k, k

x

y

d.

( ) ( )

( ) ( )

–k, k

–k, –k k, –k

k, k

x

y

____ 17. rectangle with side length 4k units and height 2k units

a.

( 2 ) ( 2 )

( –2 ) ( –2 )

–k, k

–k, k k, k

k, k

x

y

c.

(–2 ) (2 )

(–2 ) (2 )

k, k

k, – k k, –k

k, k

x

y

b.

(–2 2 ) (2 2 )

(–2 –2 ) (2 –2 )

k, k

k, k k, k

k, k

x

y

d.

( ) ( )

( ) ( )

–k, k

–k, –k k, –k

k, k

x

y

____ 18. square with side length 2k units

a.

( 2 ) ( 2 )

( –2 ) ( –2 )

–k, k

–k, k k, k

k, k

x

y

c.

(–2 ) (2 )

(–2 ) (2 )

k, k

k, – k k, –k

k, k

x

y

b.

(–2 2 ) (2 2 )

(–2 –2 ) (2 –2 )

k, k

k, k k, k

k, k

x

y

d.

( ) ( )

( ) ( )

–k, k

–k, –k k, –k

k, k

x

y

____ 19. isosceles trapezoid with height c units, bases 4d units and 2d units

a.

(–2 ) (2 )

( 0) ( 0)

d, c d, c

d,–d, x

y

c.

(–4 ) (4 )

(–2 0) (2 0)

d, c d, c

d,d, x

y

b.

(0, ) (4 )

(0, 0) (2 0)

c d, c

d, x

y

d.

(0, ) (8 )

(0, 0) (4 0)

c d, c

d, x

y

____ 20. isosceles trapezoid with height c units, bases 8d units and 4d units

a.

(–2 ) (2 )

( 0) ( 0)

d, c d, c

d,–d, x

y

c.

(–4 ) (4 )

(–2 0) (2 0)

d, c d, c

d,d, x

y

b.

(0, ) (4 )

(0, 0) (2 0)

c d, c

d, x

y

d.

(0, ) (8 )

(0, 0) (4 0)

c d, c

d, x

y

Short Answer

21. Using the figure below, write a coordinate proof for the following condition.

The diagonals of an isosceles trapezoid are congruent.

FG

D E x

y

D (0, 0), G (b, c), F (a – b, c), E (a, 0)

22. Determine whether the figure with the given vertices is a parallelogram. Use the method indicated.

; Slope Formula

23. A glasscutter needs to cut rectangular pieces of glass to make an aquarium. How can he make sure that the

glass pieces he is going to cut are rectangular in shape? Justify your reasoning.

24. An HD display measuring 1644 inches by 600 inches was erected in a stadium. Find the measure of the

diagonal of the HD display.

25. Richard wants to buy a LCD flat panel monitor measuring 14 inches by 16 inches. What is the measure of the

diagonal of the monitor?

Given each set of vertices, determine whether PQRS is a rhombus, a rectangle, or a square. List all that

apply. Explain your reasoning.

26.

27. For isosceles trapezoid ABCD, find the length of the median and .

A B

CD

15

5

68°

28. For isosceles trapezoid PQRS, L and M are the midpoints of the legs. Find LM, , and .

P Q

RS

48

26

L M

57°

29. For trapezoid GHJK, P and Q are the midpoints of the legs. Find , , and .

K J

P Q

G H

25

55

6257 °°

Use trapezoid ABCD to find each measure.

D C

L M

A B

44

96

110

55

°

°

30. Let be the median of DCML. Find , , and .

31. Let be the median of LMBA. Find , , and .

32. (Honors) A basketball court can be separated into two shapes that resemble quadrilaterals. Write a coordinate

proof to prove that the opposite sides of ABCD are congruent. All measures are approximate and given in feet.

Essay

33. (Honors) How can you determine that the portion of the tent represented by ABCD forms a rectangle? Explain

your reasoning.

34. (Bonus) Parallelogram WXYZ has vertices with coordinates , , , and .

a. If , what can you determine about the slopes of the diagonals and ?

b. What kind of parallelogram is WXYZ?

Geometry Test Squares, Rhombi, Kites, Trapezoids

Answer Section

MULTIPLE CHOICE

1. ANS: A

The diagonals of a rectangle are congruent. Set the segments equal to each other and solve for the variable.

Use the variable’s value to solve for the diagonal length.

Feedback

A Correct! B This is the value of the variable not the length of the diagonal. C Multiply, not divide, by two to find the length of the diagonal. D This is not the length of the entire diagonal.

PTS: 1 DIF: Average REF: Lesson 6-4

OBJ: 6-4.1 Recognize and apply properties of rectangles.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply properties of rectangles.

KEY: Rectangles | Properties of Rectangles

2. ANS: C

Each angle of a rectangle is a right angle. Add the given angles together and set the sum equal to 90. Solve for

the variable. Use the value of the variable to find the missing angle.

Feedback

A Which angle are you finding? B This is the value of the variable. C Correct! D Does the diagonal bisect the angles of a rectangle?

PTS: 1 DIF: Average REF: Lesson 6-4

OBJ: 6-4.1 Recognize and apply properties of rectangles.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply properties of rectangles.

KEY: Rectangles | Properties of Rectangles

3. ANS: B

All sides of a rhombus are congruent.

Feedback

A All sides of a rhombus are congruent. B Correct! C All sides of a rhombus are congruent. D Do not use properties of special triangles.

PTS: 1 DIF: Basic REF: Lesson 6-5

OBJ: 6-5.1 Recognize and apply properties of rhombi.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply the properties of rhombi. KEY: Rhombi | Properties of Rhombi

4. ANS: A

The diagonals of a rhombus bisect the angles. Also, consecutive angles are supplementary.

Feedback

A Correct! B Doubling the given angle does not give the answer. C This is the size of the given angle. D Which angle is asked for?

PTS: 1 DIF: Basic REF: Lesson 6-5

OBJ: 6-5.1 Recognize and apply properties of rhombi.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply the properties of rhombi. KEY: Rhombi | Properties of Rhombi

5. ANS: A

Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is

either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals

are congruent and perpendicular, the quadrilateral is a square.

Feedback

A Correct! B Are the angles congruent? C Remember to list all that apply. D Are the sides congruent?

PTS: 1 DIF: Average REF: Lesson 6-5

OBJ: 6-5.2 Recognize and apply the properties of squares.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply the properties of squares. KEY: Squares | Properties of Squares

6. ANS: B

Plot the vertices on a coordinate plane. Determine if the diagonals are perpendicular. If so, the quadrilateral is

either a rhombus or square. Use the distance formula to compare the lengths of the diagonals. If the diagonals

are congruent and perpendicular, the quadrilateral is a square.

Feedback

A Are the angles congruent? B Correct! C Remember to list all that apply. D Are the sides congruent?

PTS: 1 DIF: Average REF: Lesson 6-5

OBJ: 6-5.2 Recognize and apply the properties of squares.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply the properties of squares. KEY: Squares | Properties of Squares

7. ANS: C

To find the other base, substitute the given values into the formula, .

Feedback

A Do not add the median and base.

B AB is the median not a base. C Correct! D Do not subtract the median from the base.

PTS: 1 DIF: Average REF: Lesson 6-6

OBJ: 6-6.1 Recognize and apply the properties of trapezoids.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply the properties of trapezoids.

KEY: Trapezoids | Properties of Trapezoids

8. ANS: D

To find the other base, substitute the given values into the formula, ..

Feedback

A Do not subtract the base from the median. B AB is the median not a base. C Do not add the median and base. D Correct!

PTS: 1 DIF: Average REF: Lesson 6-6

OBJ: 6-6.1 Recognize and apply the properties of trapezoids.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Recognize and apply the properties of trapezoids.

KEY: Trapezoids | Properties of Trapezoids

9. ANS: A

To find the median, find the sum of the bases and then divide by two.

Feedback

A Correct! B Do not subtract the smaller base from the larger base. C How do you find the median? D Remember to divide by two.

PTS: 1 DIF: Basic REF: Lesson 6-6

OBJ: 6-6.2 Solve problems involving the medians of trapezoids.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve problems involving the medians of trapezoids.

KEY: Trapezoids | Medians | Medians of Trapezoids

10. ANS: D

To find the median, find the sum of the bases and then divide by two.

Feedback

A This is the median of ABCD. B Where is the median of ABFE located? C How do you find the median of a trapezoid? D Correct!

PTS: 1 DIF: Average REF: Lesson 6-6

OBJ: 6-6.2 Solve problems involving the medians of trapezoids.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve problems involving the medians of trapezoids.

KEY: Trapezoids | Medians | Medians of Trapezoids

11. ANS: A

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A Correct! B Are all sides the same length? C Is this a rectangle? D Rectangles have four right angles.

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

12. ANS: B

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A Are all four sides congruent? B Correct! C Is this a square? D Squares have four right angles.

PTS: 1 DIF: Basic REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

13. ANS: C

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A How many pairs of parallel sides does a trapezoid have? B Are all sides the same length? C Correct! D How many pairs of parallel sides does a trapezoid have?

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

14. ANS: D

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A What is the height of this figure? B Are all sides the same length? C Is this a rectangle?

D Correct!

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

15. ANS: A

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A Correct! B Should all sides be congruent? C What is the height of this figure? D What is the length of each side?

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

16. ANS: B

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A Are all sides congruent? B Correct! C What is the height of this figure? D What is the length of each side?

PTS: 1 DIF: Basic REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

17. ANS: C

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A What is the height of the figure? B Should all sides be congruent? C Correct! D What is the length of each side?

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

18. ANS: D

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A Are the sides congruent? B What is the length of each side? C What is the height of this figure? D Correct!

PTS: 1 DIF: Basic REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

19. ANS: A

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A Correct! B Is this an isosceles trapezoid? C What are the lengths of the bases? D Is this an isosceles trapezoid?

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

20. ANS: C

What are the properties of the given shape? Use the properties to determine what the graph should resemble.

Feedback

A What are the lengths of the bases? B Is this an isosceles trapezoid? C Correct! D Is this an isosceles trapezoid?

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.1 Position and label quadrilaterals for use in coordinate proofs.

TOP: Position and label quadrilaterals for use in coordinate proofs.

KEY: Proofs | Coordinate Proofs | Quadrilaterals

SHORT ANSWER

21. ANS:

Given:Isosceles trapezoid DEFG with

Prove:

Proof:

and

PTS: 1 DIF: Average REF: Lesson 6-7

OBJ: 6-7.3 Position and label quadrilaterals for use in coordinate proofs and prove theorems using

coordinate proofs. TOP: Prove theorems using coordinate proofs.

KEY: Proofs | Theorems | Coordinate Proofs

22. ANS:

Yes

Using the method indicated, determine if the points form a parallelogram. If the opposite sides are congruent,

the slopes of opposite sides are congruent, or the diagonals share the same midpoint, then the points form a

parallelogram.

PTS: 1 DIF: Basic REF: Lesson 6-3

OBJ: 6-3.3 Recognize the conditions that ensure a quadrilateral is a parallelogram and prove that a set of

points forms a parallelogram in the coordinate plane.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 TOP: Solve multi-step problems.

KEY: Solve multi-step problems.

23. ANS:

Make sure that the angles measure and that the diagonals are congruent.

Use the properties of a rectangle.

PTS: 1 DIF: Basic REF: Lesson 6-4

OBJ: 6-4.3 Recognize and apply properties of rectangles and determine whether parallelograms are

rectangles. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

24. ANS:

about 1750 in.

Use the Pythagorean Theorem to find the length of the diagonal.

PTS: 1 DIF: Average REF: Lesson 6-4

OBJ: 6-4.3 Recognize and apply properties of rectangles and determine whether parallelograms are

rectangles. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

25. ANS:

about 21 in.

Use the Pythagorean Theorem to find the length of the diagonal.

PTS: 1 DIF: Average REF: Lesson 6-4

OBJ: 6-4.3 Recognize and apply properties of rectangles and determine whether parallelograms are

rectangles. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

26. ANS:

Rhombus; The diagonals are perpendicular.

Plot the vertices on a coordinate plane.

Determine if the diagonals are perpendicular. If so, the quadrilateral is either a rhombus or square.

Use the distance formula to compare the lengths of the diagonals. If the diagonals are congruent and

perpendicular, the quadrilateral is a square.

Use the distance formula to compare the lengths of the opposite sides. If the opposite sides are congruent and

perpendicular, the quadrilateral is a rectangle.

PTS: 1 DIF: Basic REF: Lesson 6-5

OBJ: 6-5.3 Recognize and apply properties of rhombi and squares.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

27. ANS:

10, 68

To find the median, find the sum of the bases and then divide by two.

PTS: 1 DIF: Basic REF: Lesson 6-6

OBJ: 6-6.3 Recognize and apply the properties of trapezoids and solve problems involving the medians of

trapezoids. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

28. ANS:

37, 57, 123

To find the median, find the sum of the bases and then divide by two.

To find the adjacent angle, apply the property that the pair of base angles of an isosceles trapezoid is

congruent.

To find the opposite angle, apply the property that the opposite angles of an isosceles trapezoid are

supplementary.

PTS: 1 DIF: Average REF: Lesson 6-6

OBJ: 6-6.3 Recognize and apply the properties of trapezoids and solve problems involving the medians of

trapezoids. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

29. ANS:

40, 118, 123

To find the median, find the sum of the bases and then divide by two.

and are supplementary.

and are supplementary.

PTS: 1 DIF: Average REF: Lesson 6-6

OBJ: 6-6.3 Recognize and apply the properties of trapezoids and solve problems involving the medians of

trapezoids. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

30. ANS:

57, 125, 55

To find the median, find the sum of the bases and then divide by two.

and are supplementary.

PTS: 1 DIF: Advanced REF: Lesson 6-6

OBJ: 6-6.3 Recognize and apply the properties of trapezoids and solve problems involving the medians of

trapezoids. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

31. ANS:

83, 70, 110

To find the median, find the sum of the bases and then divide by two.

and are supplementary.

PTS: 1 DIF: Advanced REF: Lesson 6-6

OBJ: 6-6.3 Recognize and apply the properties of trapezoids and solve problems involving the medians of

trapezoids. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve multi-step problems. KEY: Solve multi-step problems.

32. ANS:

Given:

Prove: ,

D C

BA

(0, 0) (42, 0)

(42, 50)(0, 50)

x

y

Proof:

, and

Use the Distance Formula to find the lengths of the opposite sides.

PTS: 1 DIF: Basic REF: Lesson 6-7

OBJ: 6-7.3 Position and label quadrilaterals for use in coordinate proofs and prove theorems using

coordinate proofs. TOP: Solve multi-step problems. KEY: Solve multi-step problems.

ESSAY

33. ANS:

If consecutive sides of ABCD are perpendicular or if you first determine that ABCD is a parallelogram and the

diagonals are congruent, then the parallelogram is a rectangle.

Apply the properties of a rectangle.

Assessment Rubric

Level 3 Superior

*Shows thorough understanding of concepts.

*Uses appropriate strategies.

*Computation is correct.

*Written explanation is exemplary.

*Diagram/table/chart is accurate (as applicable).

*Goes beyond requirements of problem.

Level 2 Satisfactory *Shows understanding of concepts.

*Uses appropriate strategies.

*Computation is mostly correct.

*Written explanation is effective.

*Diagram/table/chart is mostly accurate (as applicable).

*Satisfies all requirements of problem.

Level 1 Nearly Satisfactory *Shows understanding of most concepts.

*May not use appropriate strategies.

*Computation is mostly correct.

*Written explanation is satisfactory.

*Diagram/table/chart is mostly accurate (as applicable).

*Satisfies most of the requirements of problem.

Level 0 Unsatisfactory *Shows little or no understanding of the concept.

*May not use appropriate strategies.

*Computation is incorrect.

*Written explanation is not satisfactory.

*Diagram/table/chart is not accurate (as applicable).

*Does not satisfy requirements of problem.

PTS: 1 DIF: Advanced REF: Lesson 6-4

OBJ: 6-4.3 Recognize and apply properties of rectangles and determine whether parallelograms are

rectangles. STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions

34. ANS:

a. The slope of is or . The slope of is or . The product of the slopes is

. Since , the product of the slopes is or , so the diagonals

of WXYZ are perpendicular.

b. Since the diagonals are perpendicular, WXYZ is a rhombus.

Assessment Rubric

Level 3 Superior *Shows thorough understanding of concepts.

*Uses appropriate strategies.

*Computation is correct.

*Written explanation is exemplary.

*Diagram/table/chart is accurate (as applicable).

*Goes beyond requirements of problem.

Level 2 Satisfactory *Shows understanding of concepts.

*Uses appropriate strategies.

*Computation is mostly correct.

*Written explanation is effective.

*Diagram/table/chart is mostly accurate (as applicable).

*Satisfies all requirements of problem.

Level 1 Nearly Satisfactory *Shows understanding of most concepts.

*May not use appropriate strategies.

*Computation is mostly correct.

*Written explanation is satisfactory.

*Diagram/table/chart is mostly accurate (as applicable).

*Satisfies most of the requirements of problem.

Level 0 Unsatisfactory *Shows little or no understanding of the concept.

*May not use appropriate strategies.

*Computation is incorrect.

*Written explanation is not satisfactory.

*Diagram/table/chart is not accurate (as applicable).

*Does not satisfy requirements of problem.

PTS: 1 DIF: Advanced REF: Lesson 6-5

OBJ: 6-5.3 Recognize and apply properties of rhombi and squares.

STA: MA.912.G.3.1 | MA.912.G.3.4 | MA.912.G.3.3 | MA.912.G.3.2

TOP: Solve problems and show solutions. KEY: Problem Solving | Show Solutions