geometry advanced fall semester exam review packet ... · pdf filegeometry advanced fall...

Name: ________________________ Class: ___________________ Date: __________ ID: A

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Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1

Multiple Choice. Identify the choice that best completes the statement or answers the question.

1. Which statement(s) may be true about the two lines shown in the diagram?I. The lines are coplanar.II. The lines are parallel.III. The lines intersect in one point.

a. I onlyb. I and II onlyc. II and III onlyd. I and III only

2. Which of the following statements is false?

a. A, B, C, and D are coplanar.b. A, B, and D are collinear.

c. BE→⎯⎯⎯

and BA→⎯⎯

are opposite rays.d. Answers B and C only

3. Given ∠BAD, and a third ray AC in the interior of ∠BAD, if m∠BAC = 129° and m∠CAD = 51° then the two angles are ? .a. supplementaryb. complementaryc. a linear paird. supplementary and a linear pair

4. If an obtuse angle is bisected, the resulting angles are _________.a. always acuteb. right anglesc. never congruentd. always obtuse

5. Name three points that are collinear.

a. points T, Q, and Rb. points T, Q, and Sc. points S, Q, and Rd. points T, S, and R

Short Answer

6. BD→⎯⎯⎯

bisects ∠ABC. Find the value of x. 7. Find the values of the variables.

Name: ________________________ ID: A

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8. Find the coordinates of the midpoint of a segment with the given endpoints. Find the length of the segment. Round decimals to the nearest tenth.

E 4, − 8ÊËÁÁ

ˆ¯̃̃ , F −6, 6Ê

ËÁÁˆ¯̃̃

Tell whether the polygon is best described as equiangular, equilateral, regular, or none of these.

9.

10.

11. Given: Area of a triangle A = 15ft2 , and base b =5ft.Find the height h.

12. Find the length of CD.

13. ∠A and ∠B are supplementary. The measure of ∠B is three times the measure of ∠A. Find m∠A and m∠B.

14. If angle ROS is acute and angle TOR is straight, then angle TOS is what kind of angle?

15. Use the diagram to name the intersection of plane LMN and plane QLS.

ID: A

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Geometry Advanced Fall Semester Exam Review Packet -- CHAPTER 1Answer Section

MULTIPLE CHOICE

1. D 2. C 3. D 4. A 5. A

SHORT ANSWER

6. 4 7. x = 25; y = 29 8. (-1,-1); about 17.2 units 9. regular 10. equilateral 11. 6 ft 12. 7 13. m∠A = 45? m∠B = 135° 14. obtuse 15. QL


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1. What is the next number in the pattern

−3, − 72 , − 4, − 9

2 , . . . ?

a. -3b. -5

c. −112

d. -7

2. What is the converse of "If it is raining, then we will not go to the beach?"a. If it is not raining, then we will go to the beach.b. We will go to the beach if and only if it is not

raining.c. If we go to the beach, then it is not raining.d. If we do not go to the beach, then it is raining.

3. "If AB +BC = 24 and AB = 10, then 10 + BC = 24" is an example of the ? .a. Symmetric property of equalityb. Substitution property of equalityc. Addition property of equalityd. Subtraction property of equality

4. Two angles ∠3 and ∠5 are each supplementary to ∠4. If m∠5 is 78°, what is m∠3?a. 102°b. 2°c. 78°d. 90°

5. Which statement about the conditional statement "If two different lines intersect, then their intersection is a point" is true?I. The converse is true.II. The statement can be written as a true biconditional.III. The statement is false.a. I onlyb. I and II onlyc. II and III onlyd. III only

6. In the diagram, ∠1 ≅ ∠2. Which of the following is not true?

a. ∠3 ≅ ∠4b. m∠7 + m∠2 + m∠4 = 180?c. m∠3 + m∠5 = m∠4d. ∠6 ≅ ∠7

7. Which inverse of the following statements is true?a. If two lines intersect to form a right angle, then

they are perpendicular lines.b. If m∠W is less than 45°, then ∠W is acute.c. If point K is the midpoint of JL, then points J,

K, and L are collinear.d. If two rays are opposite rays, then they have a

common endpoint.

8. Decide which one of the following statements is false. a. Three noncollinear points determine a plane.b. A line contains at least two points.c. Through any two distinct points there exists

exactly one line.d. Any three points lie on a distinct line.

9. Which of the following is an example of the Transitive Property?a. If y = x − 4, then x − 4 = y.b. x − 3 = x − 3c. If x = −3, then x − 4 = −3 − 4.d. If x − 3 = y and y = −4, then x − 3 = −4.

10. If PQ = 3 and PQ + RS = 5, then 3 + RS = 5 is an example of the __________.a. Substitution Property of Equalityb. Multiplication Property of Equalityc. Transitive Property of Equalityd. Reflexive Property of Equality

Name: ________________________ ID: A

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11. Identify the property of congruence.If ∠Q ≅ ∠R, then∠R ≅ ∠Q.a. Symmetric Property of Congruence c. Transitive Property of Congruenceb. Substitution Property d. Reflexive Property of Congruence

12. In the figure shown, m∠AED = 104°. Which of the following statements is false?

a. ∠AEB and∠DEC are congruent angles. c. m∠AEB = 86°b. m∠BEC = 104° d. ∠BEC and∠CED are adjacent angles.

Short Answer

13. Predict the next three numbers: 11, 15, 23, 35, ...

14. ∠1 and∠2 form a linear pair. If m∠2 = 67°, what is m∠1?

15. ∠1 and∠2 are supplementary angles. ∠1 and∠3 are vertical angles. If m∠2 = 72° , what is m∠3?

Complete with Sometimes, Always, or Never.

16. One plane ____ passes through three noncollinear points.

17. A line ____contains at least two points.

18. Two distinct points are ____ connected by two distinct lines.

19. A line passing through two distinct points in one plane ____ lies completely in that plane.

20. Two distinct planes ____ intersect in a pair of lines.

21. If two distinct lines intersect, their intersection is ____ one point.

22. Through any three distinct points there ____ exists exactly one line.

23. Skew lines ____ intersect in exactly one point.

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

24. If the point is on the line, then it is in the plane.

Inverse:

Converse: ______

Contrapositive:

ID: A

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MULTIPLE CHOICE

1. B 2. D 3. B 4. C 5. B 6. A 7. A 8. D 9. D 10. A 11. A 12. C

SHORT ANSWER

13. 51, 71, 95 14. 113° 15. 108° 16. always 17. always 18. never 19. always 20. never 21. always 22. sometimes 23. Point, Line, and Plane Postulates do not address this topic directly. 24. Inverse: If the point is not on the line, then it is not in the plane. Converse: If the point is in the plane, then it i s

on the line. Contrapositive: If the point is not in the plane, then it is not on the line.


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Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. In the figure, l Ä n and r is a transversal. Which of the following is not necessarily true?

a. ∠8 ≅ ∠2b. ∠2 ≅ ∠6c. ∠5 ≅ ∠3d. ∠7 ≅ ∠4

2. In the figure shown, HC→←⎯⎯

Ä GD→←⎯⎯

and m∠ABC = 100? Which of the following statements is false?

a. m∠CBE = 80°b. m∠DEF = 80°c. ∠DEB and∠CBE are corresponding angles.d. ∠CBE and∠GEB are alternate interior angles.

Completion. Complete each statement.

Use the diagram to complete the statement with corresponding, alternate interior, alternate exterior, or consecutive interior.

3. ∠3 and∠5 are ____________________ angles.

4. ∠2 and∠7 are ____________________ angles.

5. ∠2 and∠6 are ____________________ angles.

6. ∠4 and∠5 are ____________________ angles.

7. ∠3 and∠7 are ____________________ angles.

Use the diagram to state whether the given angles are supplementary or congruent.

8. ∠2 and∠6 are ____________________ angles.

9. ∠3 and∠5 are ____________________ angles.

Name: ________________________ ID: A

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Short Answer

10. Find the slope of the line that contains each pair of given points: (5, −2), (−8, 3)

11. Write an equation for each line that contains (4, −5) and has slope −3.

12. Write an equation for each line that has y-intercept 3 and slope −3.

13. Write an equation of the line that passes through the point P and is parallel to the line with the given equation: P(2, 6); y = 2x + 1

14. Write an equation of the line that passes through the point P and is perpendicular to the line with the given equation: P(5, 3); y = 5x + 2

Find the value of x.

15.

16.

17. Graph the equation 5x − 7y = −35.

True or False:

18. If two parallel lines are intersected by a transversal, then alternate interior angles have measures of 90 degrees.

19. If two parallel lines are intersected by a transversal, then consecutive interior angles are supplementary.

State the postulate or theorem you would use to prove that lines a and b are parallel.

20.

21. a Ä c and b Ä c

22.

23. Write an equation of the line shown.

24. In the figure below, if l and k are parallel lines, what is the value of x 1 y?

ID: A

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MULTIPLE CHOICE

1. D 2. C

COMPLETION

3. consecutive interior 4. alternate exterior 5. corresponding 6. alternate interior 7. corresponding 8. congruent 9. supplementary

SHORT ANSWER

10. − 513

11. y = −3x + 7 12. y = −3x + 3 13. y = 2x + 2

14. y = −15 x + 4

15. 23 16. 110 17.

18. False 19. True 20. consecutive interior angles converse 21. Two lines Ä to the same line are Ä. 22. alternate interior angles converse

23. y = −12 x + 2

24. 98°


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Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

1. Which statement correctly describes the congruence of the triangles in the diagram?

a. ΔABC ≅ ΔCDA d. ΔABC ≅ ΔACDb. ΔABC ≅ ΔADC e. None of thesec. ΔABC ≅ ΔDCA

Short Answer

Decide whether it is possible to prove that the triangles are congruent. If it is possible, tell which congruence postulate or theorem you would use.

2.

3.

4.

5.

6.

7.

8.

9.

Find the value of x.

10.

Name: ________________________ ID: A

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11.

12.

13.

14. Find the values of x and y.

15. Use information in the figure below to find m∠D.

Line l is the perpendicular bisector of MN .

16. Find the value of x.

17. Find m∠M.

Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?

18.

Tell which method(s) you can use to prove that the triangles are congruent. If no method can be used, write none.

19.

20.

21.

22.

ID: A

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MULTIPLE CHOICE

1. A

SHORT ANSWER

2. yes; SSS Postulate 3. yes; HL Theorem 4. no 5. yes; SAS Postulate 6. yes; AAS 7. yes; SAS 8. yes; SSS 9. Yes; SSS, reflexive property and three pairs of corresponding sides are congruent. 10. 40 11. 35 12. 21 13. 45 14. x = 12? y = 84° 15. 30° 16. 7 17. 64? 18. AAS 19. ASA 20. HL 21. HL 22. AAS


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1. Which of the following statements is false?I. Medians intersect inside a triangle.II. Perpendicular bisectors intersect inside a triangle.III. Angle bisectors intersect inside a triangle.a. I only b. II only c. III only d. II, III

2. Given: BC→←⎯⎯

is the perpendicular bisector of KM . Which statement is true?

a. C is the midpoint of KM c. ∠KBM is a right angle.b. CM = BM d. ∠BLM,∠MLC ,∠CLK,∠KLB are all right a

3. Choose the correct statement.

a. x < 10b. 10 < x < 13c. x > 13d. x = 13

4. Given: AB = AD, m∠1 > m∠2. Then, ______.a. BE > EDb. BE < EDc. AE = ECd. BE = ED

Short Answer

5. Determine whether it is possible to draw a triangle with sides of the given lengths: 1, 2, 3

6. Find the value of x.

7. For the given triangle, state the relationships between AB and DF .

Name: ________________________ ID: A

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8. Refer to the figure below.

Given: AF ≅ FC ; ∠ABE ≅ ∠EBCWhich line is a perpendicular bisector in ABC?

9. A median of ABC is ____.

10. An altitude of ABC is ____.

11. The medians of a triangle are concurrent. Their common point is the ____.

12. Refer to the figure below.

a. If BC = 15, then LN = ______.b. If AB = 3x + 5 and NM = 2x + 1, then NM = ______.

13. In the diagram, X is the incenter of ΔRTV . Find XU.

14. Given: V is the centroid of ΔRST, SU⊥RT , UT = 12, RW = 7.5, SV = 6. Find ST and UV.

15. Use the graph shown.

Find the coordinates of D, the midpoint of AC. Use the median BD to find the coordinates of the centroid P.

16. Refer to the figure. The longest segment is ____.

17. Refer to the figure. What is the largest angle that is part of a triangle in the figure?

18. Given: D is the circumcenter. Find BD.

ID: A

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MULTIPLE CHOICE

1. B 2. D 3. C 4. A

SHORT ANSWER

5. No 6. 4

7. AB Ä DF and AB = 12 DF

8. GF→←⎯⎯

9. BF 10. BD 11. centroid 12. a. 7.5

b. 7 13. XU = 5 14. 15; 3 15. D −5,0Ê

ËÁÁˆ¯̃̃ ; P −5, 2Ê

ËÁÁˆ¯̃̃

16. ML 17. ∠ACD 18. 12


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1. Which of the following pairs of numbers has a geometric mean of 44?a. 3 and 72b. 40 and 48c. 16 and 121d. 2 and 484

2. The triangles shown are similar. Which of the following is not a correct statement?

a. ABXY = BC

YZb. ΔABC ∼ ΔXYZ

c. BCYZ = AC

XY

d. CAZX = BA

YX

3. The distance between two cities on a map is 7 centimeters. The map has a scale of 1 cm : 20 km. Find the actual distance between the two cities.a. 2.85 kmb. 0.35 cmc. 0.35 kmd. 140 km

4. If ab = x

y , then which one of the following is not

necessarily true?a. ay = bx

b. a + xb + y = a

b + xy

c. ba =

yx

d.yb = x

a

Short Answer

5. Solve: x + 22 = 6

3

Complete.

6. If 53 = s

t , then t3 = ? .

7. If 29 = m

n , then 92 = ? .

8. If 5p = 4

q , then 5 + p

p = ?q .

9. Distance Across a Ravine Use the known distances in the diagram to find the distance across a ravine from Z to Y.

10. The two polygons are similar. Find x. Then find the scale factor and the ratio of the perimeters. A(-6, 2), B(2, 2), C(2, 0), D(-6, 0); k = 0.5

Name: ________________________ ID: A

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For the next four problems, use the diagram. Given: ABCD ∼ WXYZ.

11. Find the scale factor of WXYZ to ABCD.

12. Find the values of s, t, and u.

13. Find the perimeter of each polygon.

14. Find the ratio of the perimeter of ABCD to the perimeter of WXYZ.

15. Use the diagram. CDAD = ?

?

16. The two polygons are similar. Find x. Then find the scale factor and the ratio of the perimeters.

Are the triangles similar? If so, state the similarity and a postulate or theorem that can be used to prove that the triangles are similar.

17.

18.

19.

Use the diagram to find x.

20.

21.

ID: A

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MULTIPLE CHOICE

1. C 2. C 3. D 4. B

SHORT ANSWER

5. 2

6. s5

7. nm

8. 4 + q 9. 120 yds 10. −3, 1Ê

ËÁÁˆ¯̃̃ , 1, 1Ê

ËÁÁˆ¯̃̃ , 1, 0Ê

ËÁÁˆ¯̃̃ , −3, 0Ê

ËÁÁˆ¯̃̃

11. 2 12. s = 4.5, t = 16, u = 10 13. ABCD: 21;WXYZ: 42 14. 1:2

15. EDGD

16. 1; 2:3; 23

17. yes; ΔGHI ∼ ΔKJL; SAS Similarity 18. yes; ΔMON ∼ ΔQOP;AA Similarity 19. yes; ΔRSV ∼ ΔUTV;AA Similarity

20. 21 13

21. 10

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