Download Project Problem Set 3 Module 6-Special Points and Segments in

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Project Problem Set 3
Module 6-Special Points and Segments in Triangles
1. PQ is the perpendicular bisector of MN .
What is QN?
2.If mLJK  28, what is mMLK?
3. If MX  15, find MW.
Use the figure for Exercises 7 and 8.
7. Find CB.
8. Find mCAV.
9. PQ is a midsegment of ABC.
Write an equation that relates PQ and
CS.
5. Point K is the incenter of PQR.
What is mRKQ?
10. If MX  15, find MW.
6. Which must be true?
F mPQY  mRQY
G mPRZ  mRPX
H JZ  JX
J QJ  2 • JY
11. Complete the sentence. The orthocenter
is the point of concurrency of the lines
containing the _________ of a triangle.
Module 7-Proving Theories About
Parallelograms
1.The consecutive angles of a parallelogram
measure (x  30) and 4x. What is the
value of x?
5.In quadrilateral WXYZ, W  Y. Which
information would help to prove that
WXYZ is a parallelogram?
A WY  XZ
C WX  XY
B X  W
D X  Z
6. Which MUST be a square?
2.PQRS is a parallelogram. Find x.
F
H
G
J
Use the figure for Exercises 7 and 8.
3.PSTV is a parallelogram, and V is the
midpoint of PR.
7. ABCD is a parallelogram. Find the value
of x.
What is the value of PV?
8. ABCD is a parallelogram. Find mC.
4. Which quadrilateral MUST be a
parallelogram?
F
H
9. Quadrilateral RSTU is a parallelogram.
What other information would allow you
to prove that RSTU is a rectangle?
G
F Opposite angles are congruent.
J
G Opposite sides are congruent.
H The diagonals bisect the angles.
J The diagonals are congruent.
.
10. Write True or False. The quadrilateral is a
parallelogram. Explain why or why not.
12. ABCD is a rectangle. AD  15,
AC  25, and DC  20. Find BD.
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13. Write True or False. If EF || HG and
11. In the figure, JM || KL . Show that the
EH || FG , then EFGH is a rectangle.
Explain why or why not.
quadrilateral is a parallelogram for
x  3.
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Module 10—Trigonometry
1. One acute angle of a right triangle
measures 28°. To the nearest tenth, what
is the length of the side opposite that
angle if the hypotenuse measures 16
meters?
5.A wheelchair ramp has a rise from the
ground of 1 foot. The ramp has a length of
14 feet. To the nearest degree, find the
angle the ramp makes with the sidewalk.
(The figure is not drawn to scale.)
Use the figure for Exercises 6 and 7.
Use the figure for Exercises 2 and 3.
6. What is tan, sin and cos of K?
2. If XY  10 and XW  12, what is VY?
3. If XY  9 and VW  6, what is VX?
4. When the angle of elevation of the sun is
63°, a tree casts a shadow that is 27 feet
long. To the nearest foot, how tall is the
tree?
7. To the nearest degree, what is mM?
8. A 24-foot ladder forms a 76° angle with
the ground. The top of the ladder rests
against a building. To the nearest inch,
how high up the building does the ladder
reach? DRAW A PICTURE.
9. Find JK to the nearest whole number.
10. A skateboard ramp makes a 22° angle
with the ground. To the nearest foot,
how high is the ramp?