Name:______Date:______

Geometry Midterm Review

It is always helpful to draw a picture. I encourage you to do that for any problem a picture is not given. GOOD LUCK.

Part I. Fill in the blank.

  1. A line segment contains ______.
  2. If AM = MB and points A, M and B are collinear, then ______.
  3. In a triangle, the smallest angle is (where?) ______.
  4. If two parallel lines are cut by a transversal, all corresponding angles are ______.
  5. If A is between B and C and are collinear, then ______.
  6. A right triangle has (what types of angels?)______and ______.
  7. ______(7) are methods to prove triangles congruent.
  8. The intersection of two planes is a ______.
  9. In quadrant ______, the x and y coordinates are both negative.
  10. Acute angles measure ______.
  11. Equiangular triangles are also ______.
  12. Parallel lines have the same ______.
  13. The intersection of two lines is a ______.
  14. If two angles are supplements of congruent angles, then the two angles ______.
  15. Corresponding sides of congruent triangles ______.
  16. Skew lines are ______and ______.
  17. The slope of a horizontal line is ______.
  18. Two angles are complementary if ______.
  19. The angles in a triangle sum to ______.
  20. Vertical angles are ______and______.
  21. An isosceles triangle has ______and ______.
  22. An equilateral triangle has ______and ______.
  23. If a conditional statement is false, then so is its ______.
  24. The hypotenuse of a right triangle is opposite the ______.
  25. If two sides of a triangle have length 4and 6 then the third side must be ______.
  26. A(n) ______of a right triangle is the longest side.
  27. The slope of a vertical line is ______.
  28. In a triangle, the largest angle is ______.
  29. Two lines that are not parallel or skew are ______or ______.
  30. The three medians of a triangle intersect ______and ______.
  31. When two parallel lines are cut by a transversal, the exterior angles are ______or ______.
  32. If two lines are parallel, then alternate interior angles are ______.

Part II. Free response by chapter.

True or false.Chapter 1

  1. Points A, B and H are collinear. _____4. Points E, J and F are collinear. _____
  2. Point A lies on line m. _____5. Point C lines on line l. ______
  3. Points B, C and H are coplanar. _____6. Plane ABC and plane BCF intersect at point B. _____

For questions 7 – 11, refer to the diagram at the right.

  1. Name the intersection of and plane P. ______
  2. If and were drawn, what would be their intersection? ______
  3. Name the intersection of line l and . ______
  4. Name four noncoplanar points. ______
  5. Write another name for plane P. ______

For questions 12, write the following using symbols. Do not draw.

  1. a. perpendicular ______d. parallel ______g. ray KL ______
  2. line segment AB ______e. the length of line segment CD ______
  3. angle EFG ______f. the measure of angle HIJ ______
  1. Find the length of the segment with endpoints H(2, 3) and J(6, 7). ______
  1. Find the midpoint of the segment MN with endpoints M(8, 9) and N(-2, 1). ______

For questions 15 – 17, determine whether each statement is true of false.

  1. If B is between M and T, MB = BT – MT. ______
  2. If C is the midpoint of , then CT = TA. ______
  3. Every segment has only one bisector. ______
  1. If , find . ______
  1. Find bisects ______

For questions 20 – 23, refer to the figure at the right.

  1. Name two right angles. ______
  2. Name two supplementary angles. . ______
  3. Name two congruent angles that are not right angles. . ______
  4. Name the obtuse angle. . ______
  1. The measure of an angle is three times the measure of its supplement. Find the measure of the angle. _____
  1. Find the value of y. ______
  1. Find if and ______
  1. Find the value of x if if , and ______

Chapter 2

For questions 1 - 3, determine if the conclusion is true or false based on the given information.

1. Given: and are adjacent angles.

and are opposite rays.______

Conjecture: and are supplements.

2. Given:.

Conjecture: is a right angle.______

3. Given: J, K and L are collinear.

Conjecture: JK + KL = JL.______

For questions 4 - 6, write the statement in if-then form. Underline the hypothesis once, conclusion twice.

  1. Two lines intersect exactly one point. ______

5. All tigers are cats. ______

6. All right angles measure 90 degrees. ______

Write the converse, inverse and contrapositive of the conditional statement.

  1. Vertical angles are congruent. ______

Converse:______

Inverse:______

Contrapositive:______

Complete the following statements.

  1. A plane contains ______.
  2. A line contains ______.

For questions 10 – 12, name the property of equality that justifies each statement.

  1. If and , then . ______
  2. If AB = CD, then CD = AB. ______
  3. If , then .______
  1. In the conditional “If p, then q”, the q is called the ______.
  1. Find the measure of .______

Chapter 3

1. How many pairs of skew lines does the figure at the right have? ______

Refer to the figure below. State the transversal that forms each pair of angles. Then identify the special angle

pair name.

2. and ______

3. and ______

4. and ______

5. and ______

6. and ______

7. If , , and , find the angle measures. _____.

_____,_____, _____,_____,_____,_____,_____,_____,

Find the value of x and y.

8. ______9.

______

Find the value of x so that .

10.______11. ______

Chapter 4

Determine whether each statement is true or false.

  1. All isosceles triangles are acute. ______
  2. An acute triangle can be equilateral. ______
  3. A scalene triangle is never obtuse. ______
  4. A right triangle can be isosceles. ______

Use the given conditions to classify each triangle by its sides and by its angles.

5. , with WH = WO = 5 cm. ______

6. , with GB = 4 cm , BA = 3 cm. ______

Find the value of x.

7.______

______8.

Write a congruence statement for the congruent triangles in each diagram.

9. ______10. ______

Determine which postulate or theorem can be used to prove the triangles congruent.

11. ______12. ______13. ______

Always, sometimes or never.

  1. An equilateral triangle is ______an isosceles triangle.
  2. An isosceles triangle is ______an equilateral triangle.
  3. A triangle ______has one obtuse angle and one right angle.
  4. An equilateral triangle is ______an obtuse triangle.
  5. An equilateral triangle is ______an acute triangle.

Find the value of x and y.

18. ______19. ______20.______

21. What is the vertex for ______

Chapter 5

  1. Name the triangle for which is a median. ______
  1. Name an altitude of . ______
  1. Name a median to in . ______
  1. Name a perpendicular bisector ______to triangle _____.
  1. Name an angle bisector. ______to angle _____ .
List the sides of in order from longest to shortest if the angles of have the indicated measures.

6. 4x – 17x + 33x – 4______

7. 5x + 26x - 548 – 2x______

  1. Two sides of a triangle are 16 and 22 centimeters in length. Determine whether 39 centimeters can be the length of the third side? ______

9. Two sides of a triangle are 21 and 24 centimeters in length. Determine whether 40 centimeters can be the length of the third side? ______

Write the inequality relating each pair of measures.

10. 11.

Write an inequality to describe the possible values of x.

12.______13.______

Part III: Multiple Choice

Choose the best answer for each question.

Chapter 1

  1. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9).

A. 13B. 17C. 5D. 12

  1. Points A, B and D

A. determine a planeB. are collinear

C. are contained in only plane P D. are noncoplanar points

  1. What is the intersection of planes P and R.

A points A, D and BB. C. D.

  1. What is the measure of if R is between Q and T, QR = 14 and RT = 5?

A. 10B. 11C. 19D. 9

  1. Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2).

A. (3, 4)B. (2, 4)C. (4, 8)D. (1, -1)

  1. What are the sides of ?

A. B.

C. D.

  1. and are

A. adjacentB. verticalC. supplementaryD. complementary

  1. and are

A. adjacentB. verticalC. supplementaryD. complementary

  1. and are

A. adjacentB. verticalC. complementaryD. linear pair

  1. and are

A. adjacentB. verticalC. linear pairD. complementary

  1. Find .

A. 25B. 155

C. 175D. 5

12. If and , find

A. 150B. 130

C. 70D. 80

13. Find if bisects , and

A. 48B. 18

C. 9D. 24

Chapter 2

  1. Choose the converse of “If , then = .
  2. If = , then
  3. If , then
  4. If = , then = .
  5. None of these
  1. Identify the hypothesis of the statement “If today is Tuesday, then tomorrow is Wednesday.”
  2. Today is not Tuesday
  3. Today is Wednesday
  4. Today is Tuesday
  5. Tomorrow is Wednesday
  1. Identify the if-then form of the following: All cars have four wheels.
  2. If a vehicle has four wheels, then it is a car.
  3. If a vehicle is a car, then it has four wheels.
  4. If a vehicle is not a car, then it does not have four wheels.
  5. None of these
  1. Choose the statement that follows (1) and (2) by the law of detachment.

(1)Right angles are congruent.

(2) and are right angles

A. m = 90B. m = 90C. D. =

  1. Which statement represents the law of syllogism.
  2. If is a true conditional and p is true, then q is true.
  3. If and are true conditionals, then is true.
  4. If a, b and c are real numbers, then a(b + c) = ab + ac.
  5. None of these
  1. The transitive property of equality states “If a = b and b = c, then _____ “.

A. b = aB. a = cC. c = bD. b = b

7. and form a linear pair and Find

A. 62B. 28C. 118D. 90

Chapter 3

1.Given and = 72, find .

A. 108B. 72

C. 18D. 112

  1. Given , = 9x +5 and = x + 37, find the value of x.

A. 32B. 4

C. 41D. 39

  1. Given and = 3x + 28, find the value of x so that .

A. 26B. 13

C. 67D. 75

Chapter 4

  1. A right triangle must be

A. isoscelesB. acuteC. scaleneD. either isosceles or scalene

  1. Find the measures of the legs of an equilateral triangle PQR if PQ = 5x – 7 and PR = 2x + 5.

A. 39B. 13C. 12D. 4

  1. In , what is the angle opposite ?

A. B. C. D.

  1. In , if and is the hypotenuse, then is

A. acute and scaleneB. right and scalene

C. right and isoscelesD. obtuse and isosceles

  1. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle?

A. 85B. 95C. 133D. 142

  1. If , then is congruent to

A. B. C. D.

  1. Which of the following is not a postulate used to prove the congruence of two triangles?

A. ASAB. SSAC. SASD. SSS

  1. The measure of the vertex angle of an isosceles triangle is 120. That is the measure of the base angle?

A. 60B. 30C. 35D. 40

  1. Name one additional pair of corresponding parts that need to be congruent in order to prove that

by ASA.

A. B.

C. D.

Chapter 5
  1. Identify the median of .

A. B.

C. D.

  1. Identify the altitude of .

A. B

C. D.

  1. In , if and is an angle bisector, find

A. 90B. 51

C. 39D. 12

  1. What is the longest side of the figure QUAD.

A. B

C. D.

  1. In , = 6x – 8, 7x + 3, and = 3x – 7. Choose the list that shows the sides correctly ordered from shortest to longest.

A. B.

C. D.

  1. Determine which set of numbers can be the measures of the sides of a triangle.

A. 13, 10, 16B. 1, 2, 3C. 5.2, 11, 4.9D. 208, 9, 219

  1. Two sides of a triangle have lengths 15 cm and 19 cm. Which measurement can be the length of the third side?

A. 6 cmB. 4 cmC. 40 cmD. 36 cm

  1. If the sides of a triangle have measures 3x + 4, 6x – 1 and 8x + 2, find all possible values of x.

A. x > -1B. C. D. x > 0

  1. If M is the midpoint of , , JL = 10x + 2, and LK = 6x + 14, which is a possible value of x?
  2. 1
  3. 2
  4. 3
  5. 4

Properties

State the property, theorem, postulate or definition used to make the conclusion.

  1. If UV = VW, then VW = UV.______
  1. If is a right angle, then is 90.______
  1. 2(x – 50) = 2x – 100.______
  1. If and are vertical angles, then . ______
  1. If , then is a right angle. ______
  1. AB + BC = AC.______
  1. If , then .______
  1. . ______
  1. If 2x + 4 = 17, then 2x = 13.______
  1. T is the midpoint of , then .______
  1. If and , then .______
  1. If and are a linear pair, then they are supplementary.______
  1. If bisects , then .______
  1. If and are supplementary, then .______
  1. If , then .______
  1. , then .______
Algebraic Proof

1.Given:3(2x – 5) + 1 = 2(x – 3)

Prove:x = 2

StatementsReasons

1.______1.______

2.______2.______

3.______3.______

4.______4.______

5.______5.______

6.______6.______

Proofs: Extra Credit

1.Given:Prove:

F is a midpoint of

StatementsReasons

1. ______1.______

2. ______2.______

3. ______3.______

4. ______4.______

5. ______5.______

6. ______6. ______

7. ______7.______

2.Given:W is a midpoint of Prove:

StatementsReasons

1. ______1. ______

2. ______2. ______

3. ______3. ______

4. ______4. ______

5. ______5. ______

6. ______6. ______

7. ______7.______

1

Geometry Mid-Term Review