Geometry Mid-Term Exam Review Unit #1 – Unit #6 (2015-16)
Name:____________________________________________ Due _____________________
Chapter 1 Topics: Unique Line Assumption
Angle Addition Postulate
Flat Plane Assumption
Segment Addition Postulate
Line Intersection Theorem Collinear
Formulas:
Coplanar
Distance Formula
Segment Bisector
Distance between 2 numbers
Perpendicular Bisector
Midpoint Formula
Angle Bisector
Midpoint of two numbers
Supplementary Angles
Constructions:
Complementary Angles
Perpendicular Bisector & Midpoint
Linear Pair
Angle Bisector
Vertical Angles
Congruent Segment
Adjacent Angles
Congruent Angles
1. Name the three undefined geometric terms. ________________ ________________
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2. True or False. In Euclidean geometry, two different lines intersect in at most one point. Explain your answer in complete sentence form. ________________________________________________________________________________________________ 3. Use the diagram provided. The lines are labeled a, b, and c. a. Name a line containing P. b. Name 3 non-coplanar points.
____________ ____
c. Name 3 collinear points.
____________ ____________
4. S is between R and T, if RS = 7a and ST = 12a and RT = 76, find the value of a and RS. ______________ ______________ 5. Using the number line below, find ST.
______________
6. On the segment below, M is the midpoint of XY , MY = 3x + 3, and XM = 5x – 9. a. Write an equation that will help you find x.
7. Are
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b. Solve for x.
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c. Find XY
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# LS and # SL the same set of points? Explain why or why not.
__________________________________________________________________________
8. Suppose that m∠AXB = 43°. a. Name a linear pair.
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b. Name a pair of vertical angles.
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c. Find m∠CXD
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d. Find m∠BXD
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9. An angles measure is 14 times the measure of its complement. Find the measure of the angle and its complement. __________________ 10. Suppose ∠1 and ∠2 form a linear pair with m∠1 = (8j + 1)° and m∠2 = (9j + 9)° a. Find j
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b. Find m∠2
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11. Using the points A(5, -2) and B(-1, 6) calculate the following. a. Find the distance between A and B.
b. Find the midpoint of
12. In the figure below,
AB .
__________________
__________________
# DB bisects ∠ADC. What is m∠ADC? __________________
Chapter 2 Topics: Conjecture
Write a two column proof
Deductive Reasoning
Properties of Equality
Inductive Reasoning
Properties of Congruence
13. Find the measure of each numbered angle below if m∠4 = (2x + 1)° and m∠6 = (6x – 7).
____________ ____________ ____________ ____________
14. Find the measure of each numbered angle below if m∠3 = (8x + 13)° and m∠4 = (14x + 2).
____________ ____________ ____________ ____________
15. Tell whether each of the following is inductive or deductive reasoning. a. Sam notices that every morning his little brother wakes up first and runs into Sam's bedroom to wake him up. Sam goes to sleep for the night and assumes that his little brother will come in and wake him up in the morning. _________________________________________________________ b. There is a myth that the Great Wall of China is the only manmade object visible from the moon. The Great Wall is barely visible in photographs taken from 180 miles above the Earth. The moon is 237,000 miles from Earth. Therefore, the myth can't be true. _________________________________________________________ 16. What property of equality is illustrated by: If 4x + 9 = 5, then 4x = - 4.
____________________________
17. Write a two column proof. Given: B is the midpoint of Prove: AB = CD Statements
Reasons
AC and C is the midpoint of BD
1.
1.
2.
2.
3.
3.
18. Solve and prove. Given: 5(x + 3) = -7x + 195 Prove: x = 15 Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
Chapter 3 Topics: Transversals
Equidistant
Proving Lines Parallel
Parallel Lines
Distance
Parallel Planes
Alt. Ext. Angles
Alt. Int. Angles
Same side interior angles
Same side exterior angles
Point Slope Form
Slope Intercept Form
Slope
Vertical Angles
Corresponding Angles
Constructions:
Linear Pair
A line through a point parallel to a given segment A line through a point perpendicular to a given segment
19. Give an equation for a line perpendicular to the line
2 y= x"5 passing through (2, 3) in point-slope form. 3 _____________________
20. Give an equation for the line that goes through the points (1, 5) and (3, 1) in slope-intercept form. _____________________
21. Use the figure below, where m // n. If m∠1 = 140° , then find m∠8.
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22. Using the figure above, where m // n. If m∠3 = 15x + 4 and m∠6 = 11x + 15. Find m∠6.
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23. In the figure below p // q. If m∠6 = (6g + 4)° and m∠3 = (15g + 8)°. Find m∠3.
_____________________
24. Write an equation in slope-intercept form for the line with slope -5 and y-intercept of 7.
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25. Write an equation in slope-intercept form for the line through (2, - 4) and (-1, 5).
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26. Find the value of x which makes m // n.
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27. Construct the line through point P that is parallel to the given segment.
28. Construct the line through point P that is perpendicular to the given segment.
Chapter 4 Topics: Acute, Right, Obtuse Triangles
Scalene, Isosceles, Equilateral Triangles
Use distance formula to classify triangles
Triangle Sum Theorem
Exterior Angle Theorem
Triangle Congruence (SSS, SAS, ASA, AAS, HL)
CPCTC
Reflexive Property
Isosceles Triangle Theorem
Equilateral Triangle Theorem
29. Name the triangle shown below which fits each description. Choose the best answer in each case. a. scalene triangle b. isosceles triangle c. equilateral triangle 30. The extended ratio of the angles in ∆EFG is 3:5:7. Find all three angle measures.
31. What triangle congruence theorem proves that the triangles below are congruent?
_____________________ _____________________ _____________________ _______
________
________
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32. Using the diagram at the right, give the additional piece of information that would be needed to say that the two triangles are congruent by the following theorems: a. ASA Congruence Theorem ____________________ b. SAS Congruence Theorem ____________________ c. AAS Congruence Theorem ____________________
33. In the figure below, m∠M = 4t° and m∠P = 13t°, find m∠PNO.
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34. Classify ∆ABC based on its side lengths with A(-3, 4), B(-3, 9), C(1, 7). A graph is not sufficient evidence. You must show calculations that support your answer. _____________________
35. Using the figure below, find m∠A and m∠B.
_____________________ _____________________
36. Complete the missing portions of the proof below. Given: M is the midpoint of RS ; ∠URM ≅ ∠TSM. Prove: ∆RMU ≅ ∆SMT Statements
RS ; m∠URM ≅ m∠TSM.
1. M is the midpoint of
Reasons 1. Given
2.
2.
3.
3.
4.
4.
37. If ∆ABC is an isosceles triangle with vertex ∠B, then find the value of x and m∠B when m∠A = (77- x)º, m∠B = (3x + 12)º, and m∠C = (4x + 7)º. _____________________ _____________________ 38. Complete the proof below. Given: LQ ≅ NP ; ∠NLQ ≅ ∠LNP Prove: QN ≅ PL Statements
Reasons
1
1.
2.
2.
3.
3.
4.
4.
Chapter 5 Topics: Perpendicular Bisector
Angle Bisector
Median
Altitude
Circumcenter
Incenter
Centroid
Orthocenter
Calculate Centroid and Circumcenter in coordinate plane
Triangle Midsegment Theorem
Triangle Inequality Theorem
Calculate slope, midpoint, distance.
Hinge Theorem
Construct:
Angle-Side Relationships
Circumcenter, Incenter, Centroid, Median
39. List the angles of the triangle with the given vertices in order from smallest to largest. Show all of your work used in calculating the distance of each side. X(-3, -2), Y(3, 2), Z(-3, -6)
40. Find the range of measures of the third side of a triangle with side lengths 23 and 39.
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41. Is it possible to form a triangle with the given side lengths? Explain your answer. 9.9cm, 1.1cm, 8.2cm
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42. List the sides of the triangle in order from smallest to largest.
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43. State whether each statement is always, sometimes, or never true. Explain your answer. a. The medians of a triangle intersect at one of the vertices of the triangle.
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b. The angle bisectors of a triangle intersect at a point in the interior of the triangle.
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44. Name the point of concurrency of the angle bisectors of a triangle. 45. In ∆RST, if point P is the midpoint of
_____________________
RS , then PT is called what?
46. Name the point of concurrency of the altitudes of a triangle?
_____________________ _____________________
47. In ∆JKL, if point H is equidistant from
# KJ and # KL then HK
48. Points P, Q, and R are the midpoints of
JK , KL , and JL respectively. Find x. _____________________
49. Find FH.
is called what?
_____________________
_____________________
50. What is the minimum number of perpendicular bisectors needed to construct the circumcenter? _____________________ 51. In ∆ABC,
CR is a median. Find AB. _____________________
52. Construct the incenter of ∆WIN.
53. Find the coordinates of the centroid of the triangle with the following vertices. A (0, 6), B(8, 6), C(0, -8)
_____________________
54. Compare PS and PQ
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55. Find the range of values for x.
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56. Tell whether the numbers provided can be side lengths of a triangle. If so, classify by angle measure. a. 15, 18, 20
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b. 7, 8, 11
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Chapter 6 Topics: Regular Polygons
Kite
Convex
Trapezoid
Concave
Trapezoid Midsegment Theorem
Parallelogram
Polygon Angle Sum Theorem
Rectangle
Polygon Exterior Angle Sum Theorem
Square
Refer to chapter 6 quizzes for additional review!
57a. Find the sum of the exterior angles in a 19-gon.
b. Find the measure of one exterior angle of a regular 19-gon.
58a. Find the sum of the measures of the interior angles of a regular heptagon.
b. Find the measure of one interior angle in a regular heptagon.
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59. Draw a figure which is a convex nonagon.
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60. Draw a figure which is not a polygon.
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61. Answer the following True or False questions using the quadrilateral hierarchy: a. All trapezoids are parallelograms. T or F b. All rhombuses are parallelograms. T or F c. All rectangles are isosceles trapezoids. T or F d. All squares are kites. T or F 62. Use the figure at the right to identify: a. A diagonal. _______________ b. Two consecutive sides. ______________ c. Two nonadjacent vertices. _____________
63. Give the most specific name for the following quadrilaterals.
63.
a.
b.
c.
d.
Use the diagram below to find: a. m∠B b. m ∠GCD
a.
m∠B = _____________________
b.
m∠GC D =__________________
