Download Honors Geometry Lesson 6-4 through 6-6

Name: ____________________________________________ Block: __________
Date: _________ ID: A
Honors Geometry Lesson 6-4 through 6-6
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Classify the figure in as many ways as possible.
A.
B.
C.
D.
rectangle, square, quadrilateral, parallelogram, rhombus
rectangle, square, parallelogram
rhombus, quadrilateral, square
square, rectangle, quadrilateral
____
2. Which statement is true?
A. All squares are rectangles.
B. All quadrilaterals are rectangles.
C. All parallelograms are rectangles.
D. All rectangles are squares.
____
3. Lucinda wants to build a square sandbox, but she has no way of measuring angles. Explain how she can
make sure that the sandbox is square by only measuring length.
A. Arrange four equal-length sides so the diagonals bisect each other.
B. Arrange four equal-length sides so the diagonals are equal lengths also.
C. Make each diagonal the same length as four equal-length sides.
D. Not possible; Lucinda has to be able to measure a right angle.
____
4. In quadrilateral MNOP, ∠M ≅ ∠N. Which of a parallelogram, trapezoid, or rhombus could quadrilateral
MNOP be?
A. parallelogram or rhombus
C. trapezoid only
B. parallelogram only
D. any of the three
1
Name: _______________________________________________________________________
ID: A
Short Answer
5. In the rhombus, m∠1 = 15x, m∠2 = x + y, and m∠3 = 30z. Find the value of each variable. The
diagram is not to scale.
x=______
y=______
z=______
6. Find the measure of the numbered angles in the rhombus. The diagram is not to scale.
7. ABCD is a rectangle. AC = 5x – 3 and BD = x + 5. Find the value of x and the length of each diagonal.
x=______
AC=______
BD=______
2
Name: _______________________________________________________________________
ID: A
8. In quadrilateral ABCD, m∠ACD = 2x + 4 and m∠ACB = 5x − 8. For what value of x is ABCD a rhombus?
9. In quadrilateral ABCD, AE = x + 6 and BE = 3x − 18. For what value of x is ABCD a rectangle?
10. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 18x + 8, and
m∠M = 11x + 15, find m∠K.
3
Name: _______________________________________________________________________
ID: A
11. The isosceles trapezoid is part of an isosceles triangle with a 42° vertex angle.
a) What is the measure of an acute base angle of the trapezoid?
b) Of an obtuse base angle? The diagram is not to scale.
a)_____________
12. LM is the midsegment of
AB, LM and DC.
x= ________
AB= ________
b)_____________
ABCD. AB = x + 8, LM = 4x + 3, and DC = 243. What is the value of x? Find
LM=
________
4
DC=
________
Name: _______________________________________________________________________
13. Find the measures of the numbered angles in the kite. The diagram is not to scale.
_____________
_____________
_____________
14. Find the values of the variables and the lengths of the sides of this kite.
x=______
y=______
AB=______
BC=______
CD=______
5
DA=______
ID: A
Name: _______________________________________________________________________
ID: A
15. Find the values of a and b. The diagram is not to scale.
16. What is the most precise name for quadrilateral ABCD with vertices A(–5, 2), B(–3, 5), C(4, 5), and
D(2, 2)?
6
Name: _______________________________________________________________________
ID: A
Essay
17. Explain how you can determine, without measuring any angles, whether a quadrilateral is a rectangle.
Other
18. Two consecutive angles of a quadrilateral are right angles, but the quadrilateral is not a rectangle. Can the
quadrilateral be a parallelogram? Explain.
19. ABCD is a rhombus. Write a statement reason proof to show that ΔABC ≅ ΔCDA.
7
ID: A
Honors Geometry Lesson 6-4 through 6-6
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
ANS:
ANS:
ANS:
ANS:
A
A
B
D
TOP:
TOP:
TOP:
TOP:
6-4
6-4
6-5
6-6
Problem 1 Classifying Special Parallelograms
Problem 1 Classifying Special Parallelograms
Problem 3 Using Properties of Parallelograms
Problem 1 Finding Angle Measures in Trapezoids
SHORT ANSWER
5. ANS:
x = 6, y = 84, z = 3
TOP: 6-4 Problem 2 Finding Angle Measures
6. ANS:
m∠1 = 90, m∠2 = 24, and m∠3 = 66
TOP: 6-4 Problem 2 Finding Angle Measures
7. ANS:
x = 2, DF = 7, EG = 7
TOP: 6-4 Problem 3 Finding Diagonal Length
8. ANS:
4
TOP: 6-5 Problem 2 Using Properties of Special Parallelograms
9. ANS:
12
TOP: 6-5 Problem 2 Using Properties of Special Parallelograms
10. ANS:
154
TOP: 6-6 Problem 2 Finding Angle Measures in Isosceles Trapezoids
11. ANS:
69°; 111°
TOP: 6-6 Problem 2 Finding Angle Measures in Isosceles Trapezoids
12. ANS:
35
TOP: 6-6 Problem 3 Using the Midsegment of a Trapezoid
1
ID: A
13. ANS:
m∠1 = 17, m∠3 = 73
TOP: 6-6 Problem 4 Finding Angle Measures in Kites
14. ANS:
x = 9, y = 14; 11, 20
TOP: 6-6 Problem 4 Finding Angle Measures in Kites
15. ANS:
a = 115, b = 71
TOP: 6-6 Problem 1 Finding Angle Measures in Trapezoids
16. ANS:
parallelogram
TOP: 6-4 Problem 1 Classifying Special Parallelograms
ESSAY
17. ANS:
[4]
Shows enough properties that do not require angle measurement and concludes,
based on those properties, that the quadrilateral is a rectangle. Sample: Measure to
show diagonals bisect each other. This makes the quadrilateral a parallelogram.
Measure to show that diagonals are congruent. This makes the parallelogram a
rectangle.
[3]
demonstrates understanding of exercise, but omits one property needed to
conclude quadrilateral is parallelogram
[2]
gives way of determining that quadrilateral is rectangle, but includes angle
measurement (such as making right angles)
[1]
gives only one step necessary for concluding quadrilateral is rectangle
TOP: 6-5 Problem 3 Using Properties of Parallelograms
OTHER
18. ANS:
No; if it were a parallelogram, then the fact that it has two consecutive right angles would mean that it
has four right angles and would have to be a rectangle.
TOP: 6-5 Problem 1 Identifying Special Parallelograms
19. ANS:
AB ≅ CD and BC ≅ DA by the definition of rhombus. AC ≅ AC by the Reflexive Property, so
ΔABC ≅ ΔCDA by SSS.
TOP: 6-5 Problem 2 Using Properties of Special Parallelograms
2