Study Guide for the 3rd Nine Weeks Test

Geometry

  1. What is the inverse of the following statement?

If the measure of an angle is between 90° and 180°, then it is an obtuse angle.

  1. Let p = The degree measure of an angle is between 0° and 90°.

Let q = It is an acute angle.

Argument:

If the degree measure of an angle is between 0° and 90°, then it is an acute angle.

The degree measure of an angle is not between 0° and 90°.

Therefore, the angle is not an acute angle.

Write the symbolic representation of the argument above.

  1. The Venn diagram below shows the types of novels the literature club members read during their summer break.

Which of the following is NOT supported by the information in the Venn diagram?

  1. 21 members read both an adventure novel and a romance novel
  2. 26 members read all three types of novels
  3. 64 members read only an adventure novel or a mystery novel
  4. 67 members read a romance novel
  1. Shade the area of the Venn Diagram that represents some cameras are cell phones.
  1. What can be concluded from the following two statements below?

Statement 1: All foreign cars are expensive.

Statement 2: My car is a foreign car.

Conclusion: ______

  1. Given the information in the figure below, what are the values of x and y?

  1. What is the length (to the nearest tenth) of side BC of ΔABC in the graph below?

  1. A line segment AB has endpoints A(-3, 5) and B(5, -6). What are the coordinates of the midpoint of AB?
  1. A line passes through the points (6, -2) and (5, 3).
  1. What is the slope of a line that is parallel to this line?
  2. What is the slope of a line that is perpendicular to this line?
  1. What does the figure show the construction of?
  1. What is the value of x that would justify m||n?
  1. In ΔABC, the measure of angle A = 48° and the measure of angle B = 93°. List the three sides of ΔABC in order from shortest to longest side.
  1. In ΔDEF, side DE = 6; side EF = 13; side DF = 9. Which angle is the largest?
  1. Write the range of the possible lengths of the third side of a triangle if two of the sides have length measures of 3 and 12.

What could be used to prove ΔPQR is congruent to ΔPSR?

A. SAS B. ASA C. SSS D. HL

  1. Complete the proof.

  1. What is the length of side MN?

  1. What value of x make

Which can prove that ΔDEC and ΔBAC are similar?

  1. SAS B. AAS C. AA D. SSS
  1. Which of the sets of lengths could represent the measures of the sides of a right triangle?
  1. 3, 5, 8
  2. 5, 12, 15
  3. 8, 10, 16
  4. 20, 21, 29
  1. A ladder leans against a building. The foot of the ladder is 6 feet from the building. The ladder reaches a height of 14 feet from the building. What is the length of the ladder to the nearest foot?
  1. From a point on the ground 25 feet from the foot of a tree, the angle of elevation of the top of the tree is 32º.Find to thenearest foot,the height of the tree.
  1. Find the length of the shorter leg.
  1. The bottom end of a ramp at a warehouse is 10 feet from the base of the main dock and is 11 feet long.

How high is the dock? (Be sure to draw a picture.)

  1. Determine whether the given lengths form a Right Triangle: 18, 30, 24
  1. MNOP is a parallelogram. If NR = 3x + 2 and RP = x + 14, find x and NR.
  1. MNOP is a parallelogram. If mMPO = 9x + 2 and mPON = 5x + 10, find x and mPON.
  1. In rhombusMATH,MH=y+ 8 and
    HT= 4y- 7.Findthe measure of MA.
  1. Find the measure of angle BOX.
  1. Find the sum of x, y and z.
  1. An exterior angle of a regular polygon has a measure of 40°. What is the sum of the measures of the interior angles?
  1. Pentagon ABCDE is an outline of the front of a house. Find the measure of each interior angle.
  1. The below figure is an outline of a camping tent. Find the unknown angle measures.
  1. If you have a windmill with 4 blades and arc length of 36π, what is the length of the blades?
  1. A ceiling fan has 8 blades. Each blade is 16 inches. What is the arc length between the blades?
  1. Circle O has a central angle of 120° and the radius is 6. Find the area of the shaded sector of Circle O.
  1. The circle below has a diameter perpendicular to a chord. Find x.
  1. What is the value of x in the circle below?
  1. Mrs. Smith wants to purchase a cover for their new circular pool. She needs to know the radius of the pool, but she does not want to get wet to take the measurements. She is standing 4 feet from the pool and 12 feet from the point of tangency.Find the radius of the pool.
  1. Write the equation of the circle below.
  1. Given circle W with a chord CD passing through point W given the endpoints C(4, 7) and D(4, -5) with an area of 144 ft2. Write the standard equation of Circle W.
  1. Given: Circle W W(-4,6) and Radius = 10 units. Which point lies on circle W?
  1. (0,4) B. (2,10) C. (4,0) D. (6,16)
  1. Line BD is tangent to the circle at point C and the measure of arc AC = 110. What is the measure of angle DCE?
  1. For what values of x, y, and z are the triangles similar?
  1. What is the radius of the circle shown?
  1. An equilateral triangle with a side length of 10 is folded in half. What is x, the height of the equilateral triangle?

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