Module 6-Special Points and Segments in Triangles

Project Problem Set 3

Module 6-Special Points and Segments in Triangles

1. is the perpendicular bisector of 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.

5.Point K is the incenter of PQR.
What is mRKQ?

6.Which must be true?

FmPQY mRQY

GmPRZ mRPX

HJZJX

JQJ 2 • JY

9. is a midsegment of ABC.
Write an equation that relates PQ and CS.

10. If MX 15, find MW.

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?

2. PQRS is a parallelogram. Find x.

3. PSTV is a parallelogram, and V is the midpoint of

What is the value of PV?

4.Which quadrilateral MUST be a parallelogram?

5. In quadrilateral WXYZ, W Y. Which information would help to prove that WXYZ is a parallelogram?

AWYXZCWXXY

BX WDX Z

6.Which MUST be a square?

Use the figure for Exercises 7 and 8.

7.ABCD is a parallelogram. Find the value of x.

8.ABCD is a parallelogram. Find mC.

9.Quadrilateral RSTU is a parallelogram. What other information would allow you to prove that RSTU is a rectangle?

FOpposite angles are congruent.

GOpposite sides are congruent.

HThe diagonals bisect the angles.

JThe diagonals are congruent.

10.Write True or False. The quadrilateral is a parallelogram. Explain why or why not.

______

11.In the figure, . Show that the

quadrilateral is a parallelogram for
x 3.

______

12.ABCD is a rectangle. AD 15,
AC 25, and DC 20. Find BD.

______

13.Write True or False. If and
, then is a rectangle. Explain why or why not.

______

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?

Use the figure for Exercises 2 and 3.

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?

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.

6.What is tan, sin and cos of K?

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?