Geometry Fall Final Review
*Chapter 1.1 Points Lines Planes Use the figure to name each of the following: 1. five points
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*Chapter 1.2 Line Segments and Distance Find the length of the following: 11. Segment AB
12. Segment BC
2. two lines
3. two planes
4. point on line BD
Draw and label each of the following: 5. a segment with endpoints M and N
13. B is a point between points A and C, segment AC = 15.8, and segment AB = 9.9. Find the length of segment BC. (Draw a picture).
14. Find the length of segment NP.
6. three coplanar lines that intersect in a common point
7. ray with endpoint F that passes through G
15. K is the midpoint of segment JL, JL = 4x - 2, and JK = 7. Find x, the length of KL, and JL.
8. two lines that do not intersect
1.3 Locating Points and Midpoints
Use the figure to name each of the following:
Find the coordinates of the midpoint of each segment: 16. AB with endpoints A (4, -6) and B (-4, 2)
9. a line that contains A and C 10. a plane that contains A, D, and C
17. CD with endpoints C (0, -8) and D (3, 0)
Geometry Fall Final Review
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*Chapter 1.4 Angle Measures 18. ∠A is an acute angle. ∠O is an obtuse angle. ∠R is a right angle. Put ∠A, ∠O, and ∠R in order from least to greatest by measure. 19. a. Which point is the vertex of ∠BCD? b. Which rays form the sides of ∠BCD?
24. L is in the interior of ∠JKM. Draw and label a picture then answer the following: Given: m∠JKL = 42° and m∠LKM = 28° Find m∠JKM
25. Ray BD bisects ∠ABC. Draw and label a picture then answer the following: 26. Given: m∠ABD = (6x + 4) ° and m∠DBC = (8x - 4)°. Find m∠ABD
*Chapter 1.5 Angle Relationships 20. Correctly name all 3 angles in the diagram as acute or obtuse. 1. 2. 3.
Tell whether the angles are adjacent, a linear pair, or vertical angles.
27. ∠1 and ∠2
Use the protractor to find the measure of each angle. Then classify each as acute, right, or obtuse.
28. ∠2 and ∠5 29. ∠1 and ∠3
30. ∠8 and ∠3 *Chapter 1.6 Two-Dimensional figures 31. Find the area and perimeter of each figure. a. b. c.
21. ∠VXW
22. ∠TXW
23. ∠RXU
Geometry Fall Final Review
*Chapter 3.1 Parallel Lines and Transversals Identify each of the following using the figure:
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Identify the type of angle pair given: (corresponding, alternate interior, alternate exterior, same side interior)
1. a pair of perpendicular segments
9. ∠6 and ∠8
2. a pair of skew segments
10. ∠2 and ∠3
3. a pair of parallel segments
11. ∠2 and ∠4
4. a pair of parallel planes
12. ∠5 and ∠4
Write all possible answers for each of the following: *Chapter 3.2 Angles and Parallel Lines 13. Solve for x:
5. alternate interior angles
14. Solve for x:
6. alternate exterior angles
7. corresponding angles 15. Solve for x 8. same-side interior angles
Geometry Fall Final Review
16. Solve for x
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*Chapter 3.4 Equations of Lines Write the equation of the line that: 27. passes through (4, 7) and (-2, 1) in slopeintercept form.
Use the figure to find the value of all the missing angles: 17. ∠1= ________ 18. ∠2= ________ 19. ∠3= ________ 20. ∠4= ________ 21. ∠5= ________ 22. ∠6= ________ 23. ∠7= ________ *Chapter 3.3 Slopes of lines 24. Find the slope of the given line. Say if it is positive, negative, zero or undefined.
28. passes through ( -4, 2) with slope ¾ in point-slope form. 29. Write the equation of the line that has a slope of -3/4 and passes through (-2, 5) in point-slope form. 30. Write an equation of the line that has a slope of -4 and y-intercept in slope-intercept form.
*Chapter 3.6 Perpendiculars and Distance 31. Find the shortest distance between the line with points (-2, 0) and (4,8) and point (5,1)
32. Find the shortest distance between the parallel lines: y = -x and y = -x - 4
Determine if the lines are parallel, perpendicular or neither by comparing their slopes. 25. HJ: H (3, 2) , J(4,1) and KM: K (-2, -4), M(-1, -5) 26. LM: L(-2, 2), M( 2, 5) and NP: N(0, 2) , P(3, -2)
Geometry Fall Final Review
*Chapter 4.1 Classifying Triangles Classify each triangle as acute obtuse, right, equiangular, equilateral, isosceles or scalene. 1. 2.
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*Chapter 4.2 Angles of Triangles
6. Find m∠ABC
7. Find m∠ACD
8. Find m∠CAD 3.
4.
9. Find m∠L
*Chapter 4.3 Congruent Triangles 5. Solve for x and find the side lengths of the triangle:
Identify the congruent corresponding parts:
a.
b. 10. ∠Z ≅ _______ 11. YZ ≅ _______ 12. ∠P ≅ _______ 13. ∠X ≅ _______ 14. NQ ≅ _______ 15. PN ≅ _______
Geometry Fall Final Review
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*Chapter 4.4-4.5 SSS, SAS, ASA, AAS, HL Determine if the two triangles are congruent by SSS, SAS, ASA, AAS, HL or not congruent. 16. 17.
18.
19.
20.
21.
*Chapter 4.6 Isosceles and Equilateral Triangles 26. Find m∠D
27. Find m∠N
28. Solve for n
29. Find m∠H
30. Solve for side ST 31. Solve for side RT
22.
23.
24.
25.
Geometry Fall Final Review
*Chapter 5.1 Bisectors of Triangles Circumcenter and Incenter
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6. P is the circumcenter of the triangle. a. PS
1. Find FG
2. Find KL b. XT c. RS
3. Find TU
4. Find m∠PYM 7. A is the incenter. Find the following: a. find ∠AYG b. ∠YLA c. Find ∠YGL d. find ∠QPK
5. A is the circumcenter.
8. K is the incenter. Find a. m∠JHK b. m∠LKH a. solve for x
b. find ∠QPK
c. find ∠URT
d. Find AU
*Chapter 5.2 Medians and Altitudes 9. W is the centroid and BD=87 and WE=38. Find a. BW b. CW c. CE
Geometry Fall Final Review
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10. K is the centroid. NQ = 6. Find: a. KM
12. List the angles that are
b. KQ
b. less than ∠9
c. LK
c. more than ∠3
d. LR
d. more than ∠6
a. less than ∠1
e. NK f. PM
*Chapter 5.3 Inequalities in one triangle 11. List the sides and angles from shortest to longest. a.
b.
*Chapter 5.5 Triangle Inequality 13. Determine if a triangle can have the given side lengths: 2,3,4
4,8,11
9,10,20
6,7,12
5,5,10
1,5,6
14. Give the range of the 3rd side for each triangle: 5,6
7,2
6,1
4, 6
10,3
12, 11
c.
d.
Geometry Fall Final Review
*Chapter 5.6 Inequalities in two triangles.
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19.
Compare the given measures. 15. AB and DE
20. 16. ∠I and ∠L
21. 17. PS and PQ
Solve for the range of possible x values. 18.