Homework Worksheets: Chapter 6
HW#30: Problems #1 – 11
1.) All of the following statements are true except:A. Opposite sides of a parallelogram are congruent.
B. Opposite angles of a parallelogram are congruent.
C. Diagonals of a parallelogram are congruent.
D. Diagonals of a parallelogram bisect each other.
E. Opposite sides of a parallelogram are parallel. / 2.) A regular polygon has 10 sides. Find the measure of each interior angle.
A. 360˚
B. 36˚
C. 1440˚
D. 144˚
E. 180˚
3.) Quadrilateral ABCD is a parallelogram. Which of the following must be true?
A. AB = BC
B. BC = CD
C.
D. AC = BD
E. / 4.) The measure of an exterior angle of a regular polygon is 18˚. Find the measure of each interior angle.
A. 18˚
B. 162˚
C. 180˚
D. 360˚
E. 3240˚
5.) Identify a counterexample to the given statement:
Two planesalways intersect at a line.
A. No counterexample needed; this is true.
B. Two perpendicular lines.
C. Two parallel lines.
D. Two intersecting planes.
E. Two parallel planes. / 6.) Scalene triangles have ______congruent sides.
A. 0
B. 1
C. 2
D. 3
E. not enough information to conclude
7.) Simplify each expression:
a) b)
c) d)
For #9-11, solve each equation by factoring: / 8.) Simplify each expression:
a) b)
c) d)
9.) / 10.) / 11.) 12x3 – 75x = 0
HW #31: Problems #12-24
Quadrilateral MNOP is a parallelogram.
(Diagram for #13-14) / 12.) Name the property of parallelograms that justifies the statement: MN = OP
A. Opposite sides of a parallelogram are congruent.
B. Opposite angles of a parallelogram are congruent.
C. Diagonals of a parallelogram bisect each other.
D. Opposite sides of a parallelogram are parallel.
E. Consecutive sides of a parallelogram are congruent.
13.) Name the property of parallelograms that justifies the statement:
A. Opposite sides of a parallelogram are congruent.
B. Opposite angles of a parallelogram are congruent.
C. Diagonals of a parallelogram bisect each other.
D. Opposite sides of a parallelogram are parallel.
E. Consecutive sides of a parallelogram are congruent. / 14.) Name the property of parallelograms that justifies the statement:
A. Opposite sides of a parallelogram are congruent.
B. Opposite angles of a parallelogram are congruent.
C. Diagonals of a parallelogram bisect each other.
D. Opposite sides of a parallelogram are parallel.
E. Consecutive sides of a parallelogram are congruent.
15.) Find each quantity for a regular decagon:
Sum of Exterior Angles:
Each Exterior Angle:
Each Interior Angle:
Sum of Interior Angles: / 16.) All of the following information is enough to state that a quadrilateral is a parallelogram except:
A. Both pairs of opposite sides are congruent.
B. Both pairs of opposite angles are congruent.
C. One pair of opposite sides of is both congruent and parallel.
D. One pair of opposite sides is parallel, the other pair of opposite sides is congruent.
E. Both pairs of opposite sides are parallel.
17.) Solve for xby factoring:
2x2 – 6 = -x / 18.) Solve for xby factoring:
16x3 – 12x2= 18x / 19.) Solve for x:
x2 + x2 = 62
19.) Solve for x:
(2x)2 + x2 = 2 / 20.)Find the equation of the line that passes through (-3, 4) and
(8, 1) in standard form. / 21.) Find the equation of the line in slope-intercept form that passes through (2, 5) and is parallel to y = 2x + 1
For #22-24, a trapezoid and its median are shown. Solve for x.
22.)
/ 23.)
/ 24.)
HW #32: Problems #25–33
25.) In the figure below, .
Which addition information would be enough to prove that ?
A. B.
C. D.
E. / 26.) Identify a counterexample to the following statement:
If one pair of opposite sides of a quadrilateral is parallel, then the quadrilateral is a parallelogram.
A. rectangle
B. rhombus
C. square
D. trapezoid
E. parallelogram
27.) All of the following are examples of parallelogramsexcept:
A. rhombus B. trapezoid
C. square D. rectangle
E. none of the above / 28.) The measure of each interior angle of a regular polygon is 140˚. What kind of polygon is it?
A. a regular pentagon B. a regular hexagon
C. a regular octagon D. a regular nonagon
E. a regular decagon
29.) Solve by factoring:
3x2 – 5x = 2 / 30.) Solve:
x2 + = (3x)2 / 31.) Find the equation of the line passing through (6, -2) and perpendicular to y = 3x – 5.
32.)Simplify:
a) b) / 33.) Simplify:
HW#33: Problems #34-44
34.) The perimeter of is 22in.
QR is 3in longer than RS. Find QR and RS. / 35.) Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, ABCD mustbe ______.
A. a square B. a rhombus
C. a rectangle D. a trapezoid
E. equilateral
For questions #36-37, solve by factoring.
36.)8x3 + 4x2 = 84x / 37.)
For questions #38-39, simplify:
38.) / 39.)
For #40-42, a trapezoid and its median are shown. Solve for x.
40.)
/ 41.)
/ 42.)
For 43-44, write the equation of each line described.
43.) Write the equation of the line in slope-intercept form that passes through the points
(-1, 6) and (-2, 4). / 44.) Write the equation of the line in standard form whose x-intercept is -4 and whose y-intercept is 3.
HW #35: Problems #45-56
45.) is equilateral. If and , solve for x and y. / 46.) The measure of an exterior angle of a regular polygon is 60˚. What is the sum of the measures of the interior angles?
A. 120˚
B. 180˚
C. 360˚
D. 540˚
E. 720˚
For #47-52, write the letter of every special quadrilateral that has the given property.
A Parallelogram B Rectangle C Rhombus D Square E Trapezoid
47.) two pairs of adjacent sides are congruent / 48.) diagonals are perpendicular / 49.) opposite angles are congruent
50.) diagonals are congruent / 51.) two pairs of opposite sides are parallel / 52.) all angles are right angles
For 53-56, write the equation of each line described.
53.)The line passes through the point (-6, -2) and is perpendicular to the line whose equation is
3x + 2y = 8. / 54.) The line passes through the point (8, -1) and is parallel to the line whose equation is
5x – 4y = 6.
55.) The line is parallel to the line 2x – 4y = 12 and passes through the point (-6, -8). / 56.) The line is perpendicular to the line whose equation is 4x - 8y = 24 and passes through the point (-2, 8).