Name___________________________________________ Date______________ Period ______
Geometry – April Break Assignment
Mrs. Klein
Assignment Directions:
Part 1 & 2 – Complete all work on loose leaf, keep your work in order. You must show all work
or give an explanation/definition where no work is necessary.
Part 3 – Complete all work on graph paper. Keep your work in order.
Part 4 & 5 - Complete all work on loose leaf. Keep your work in order.
NO WORK = NO CREDIT!! Staple all of your work together, in order, with this page being the first.
If the work is not stapled (with a staple) you will lose 5 points. Fill in all your answer below (neatly).
Absolutely no late assignments will be accepted.
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Part 2 –
1) ___________________
2) ___________________
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Part 3 – Show all work on graph paper.
Part 4 –
1) a) ___________________
b) ___________________
c) ___________________
d) ___________________
1) a) ___________________
b) ___________________
Part 5 –
Name ___________________________________________
(Do not hand in the questions)
April Break Assignment
Part 1:
1) Find in radical form the distance between the points whose coordinates are (3,8) and (-1, 9):
(1)
(2)
(3)
(4)
2) Find the slope of the line which passes through the two points (6,3) and (-9,5):
(1)
(2)
(3)
(4)
3) Find the coordinates of A’, the image of A(6, -7), after a reflection in the x-axis.
(1) (-6, -7)
(2) (6,7)
(3) (-7, 6)
(4) (7, -6)
4) What is the contrapositive of the statement
(1)
(2)
(3)
(4)
5) The measures of two consecutive angles of a parallelogram are represented by (6x + 22) and
(4x – 42). What is the value of x?
(1) 10
(2) 20
(3) 90
(4) 82
6) In the diagram to the right,
(1) 36 o
(2) 144 o
(3) 90 o
(4) 54 o
and m<PLN = 36o. Find m<MLP.
7) The point of concurrency of the three medians of a triangle is called the:
(1) orthocenter
(2) centroid
(3) incenter
(4) circumcenter
8) Determine the slope of a line that is parallel to the straight line whose equation is
(1)
(2)
(3)
9) Which set of integers represented a Pythagorean triplet?
(1) 24,26,28
(2) 7,24,25
(3)5,6,7
(4)
(4) 8,19,21
10) Two triangles are similar. The lengths of the sides of the smaller triangle are 3,5 and 7. The
shortest side of the larger triangle is 15. Find the length of the longest side of the larger
triangle.
(1) 21
(2) 14
(3) 55
(4) 35
11) In square CDEF, the length of side DE is 20. Find the length of the diagonal DF.
(1)
(2)
(3) 10
(4) 40
.
12) In the diagram,
used to prove that
(1) ASA
and C is the midpoint of AE. Which method could be
(2) HL
(3) SSS
(4) SAS
13) Find the measure of each interior angle of a regular pentagon.
(1) 100 o
(2) 120 o
(3) 108 o
(4) 110o
14) Which of the lengths could be the sides of a triangle?
(1) 12, 5, 17
(2) 12, 7, 20
(3) 5, 13, 17
(4) 6, 12, 20
15) Find the measure of <C.
(1) 50 o
(2) 59 o
(3) 62 o
(4) 100 o
16) Find the equation of the circle with a center at (2,1) and a radius of 6.
(1) (x – 2)2 + (y – 1)2 = 36
(3) (x + 2)2 – (y + 1)2 = 6
2
2
(2) (x – 2) + (y + 1) = 36
(4) (x + 2)2 + (y + 1)2 = 6
17) Find the value of x:
(1) 177
(2) 66
(3) 129
(4) 51
18) In the diagram, DE // AC. If BD = 4, AD = 10, and BE = 6, find the length of CE.
(1) 12
(2) 15
(3) 18
(4) 20
19) Which statement is logically equivalent to: “If the sun is shining, then I do not need an umbrella”?
(1) If I do not need an umbrella, then the sun is shining.
(2) If the sun is not shining, then I do not need an umbrella.
(3) If I need an umbrella, then the sun is not shining.
(4) If the sun is not shining, then I need an umbrella.
20) If the length of one base of a trapezoid is 40, and the length of the other base is 60, the
length of the midsegment is:
(1) 45
(2) 50
(3) 55
(4) 58
21) In the diagram, MA // TH, and transversal GRES intersects the parallel lines at points R and E.
If m<ARE= 55o, find m<REH.
(1) 125 o
(2) 55 o
(3) 35 o
(4) 115 o
22) In right triangle PQR, altitude QS is drawn to the hypotenuse PR. If QS = 12 and PS = 8,
find the length of SR.
(1) 10
(2) 14
(3) 16
(4) 18
23) In circle O, chords AB and CB are drawn. If m
(1) 25 o
(2) 50 o
(3) 75 o
(4) 100 o
and m
, find m<ABC.
24) Which of the following is the equation of a straight line that passes through the point (1,5)
and has a slope of – 2:
(1) y = – 2x – 3
(2) y = – 2x + 4
(3) y = – 2x + 7
(4) y = 2x – 5
25) Straight line CD is perpendicular to straight line EF. If the slope of CD is
slope of EF is:
(1)
(2)
26) The letter A has:
(1) Point Symmetry
(3) Vertical Line Symmetry
(3)
, then the
(4)
(2) Horizontal Line Symmetry
(4) None of the Above
27) In the accompanying diagram, points T, U, and V are the midpoint of the three sides of
If QR = 10, RS = 16, and QS = 24, find the perimeter of
(1) 13
(2) 24
(3) 25
(4) 40
28) Given
with AB = 6, BC = 23, and CA = 18, which of the following statements is true?
(1) <A is the largest angle
(2) <B is the smallest angle
(3) <C is the largest angle
(4) <B is the largest angle
29) Which is not a property of the rectangle?
(1) the opposite sides are parallel
(3) the diagonals are perpendicular
(2) the opposite angles are congruent
(4) the diagonals are congruent
30) In a rectangular prism, the length is 30 feet, the width is 18 feet, and the height is 40 feet.
The volume of this rectangular prism is:
(1) 12,000 ft3
(2) 20,000 ft3
(3) 21,600 ft3
(4) 32,000 ft3
31) In the accompany diagram, quadrilateral ABCD is a parallelogram.
The coordinates at point C are:
(1) (ab, c)
(2) (a – b, c)
(3) (c, a + b)
(4) (a + b, c)
32) One method to prove that a quadrilateral is a parallelogram is to show that:
(1) the diagonals bisect each other
(2) the diagonals are perpendicular
(3) one pair of opposite sides is congruent
(4) one point of opposite sides is parallel
33) In the accompanying diagram, name a single point which is in the
interior of <PQR and at the same time in the exterior of <SQR.
(1) Point U
(2) Point T
(3) Point V
(4) Point R
34) In the accompanying diagram, three points which are collinear points are:
(1) Points C, B and A
(2) Points B, C and D
(3) Points A, B and D
(4) Points C, A and D
Part 2:
1) In the diagram, one-half of a circle is drawn inside rectangle ABCD. If radius OB = 10 in.
find the area of the shaded region. Leave your answer in terms of .
2) If the perimeter of a square is 80 meters, find the area of the square.
3) In parallelogram ABCD, side DC = 50 meters, side AD = 18 meters, and m<D = 30 o.
AE is an altitude drawn to side DC. Find the area of the parallelogram ABCD.
4) In the diagram below, lines JN and BT intersect at E. If m<JET = 5x + 10, and
m<BEN = 3x + 40, find m<BEN.
5) In the diagram below, DEG is a straight line and ray EF is drawn. If m<DEF = 12x – 18
and m<FEG = 5x + 11, find m<FEG.
Part 3:
1) Given Triangle ABC, with coordinates A(1, -3), B (2, -7) and C(6, -4)
a) Graph and label
.
b) Graph and state the coordinates of
, the image of
in the y-axis.
c) Graph and state the coordinates of
, the image of
translation,
d) Graph and state the coordinates of
, the image of
dilation,
after a reflection
after a
after a
Part 4:
1) If the radius of the circular base of a right cylinder is 8 inches and the height of the cylinder
is 20 inches, answer each of the following questions. Show all formulas and all work. Leave
any answer which involves , in terms of .
a) Find the area of the circular base of the cylinder.
b) Find the lateral area of the cylinder.
c) Find the surface area of the cylinder.
d) Find the volume of the cylinder.
Part 5:
1) In right triangle DEF, FG is the altitude drawn to the hypotenuse DE. The length of DG
is 15 units less than the length of GE.
a) If GE = x, write an expression for the length of DG in terms of x.
b) If FG = 10, find the length of GE.