Download Basic Geometry

Midterm
Basic Geometry
Midterm Review – Vocabulary
Date: _____________
Time: _____________
acute angle
adjacent angles
angle
betweenness
collinear
complementary
congruent
coplanar
degrees
distance
exterior
interior
line
line segment
linear pair
midpoint
obtuse angle
opposite rays
perpendicular
plane
point
ray
right angle
supplementary
vertex
vertical angles
protractor
Choose from the terms above to complete each sentence.
1. Two lines are _________________ if they intersect to form a right angle.
2. Two angles are _________________ if their measures have a sum of 90°.
3. When two rays intersect with a common endpoint a(n) _________________is formed.
4. The ________________ is the point located halfway between the endpoints of a segment.
5. _________________ are nonadjacent angles formed by the intersection of two lines.
6. Two angles are _________________ if their measures add up to 180°.
7. Two angles are called _________________ if they share a common side and a common vertex
(and are right next to each other).
8. A(n) _________________ is an angle whose measure is less than 90°.
9. Two segments are _________________ if they have the same measure.
10. Two angles are _____________________ if their measures add up to 90°.
11. A(n) _________________ is an angle whose measure is more than 90°.
12. The units of measure of an angle is __________________.
13. The tool used to measure angles is called a(n) ________________________.
14. A(n) ____________________ goes on forever in both directions.
15. A(n) ____________________ has an initial point and goes on forever in one direction.
16. A(n) ____________________ has a starting point and an ending point (called endpoints).
Chapter 1: Reasoning in Geometry
1) Find the next two numbers in each sequence.
a) 3, 5, 9, 15, _____, _____
b) -8, -3, 2, 7, _____, ______
c) 5, 1, -3, -7, _____, _____
2) Identify the hypothesis and conclusion of the following statement.
a) If the sum of two angles is 90°, then the angles are complementary.
Hypothesis: ______________________________________________
Conclusion: ______________________________________________
b) If you do not finish your vegetables, then you may not have dessert.
Hypothesis: ______________________________________________
Conclusion: ______________________________________________
3) Tell whether each statement is true or false. If it is false, give a counterexample.
a) If a number is even, then it is divisible by 2. ______
b) If an animal is a dog, then it has spots. ______
c) All birds can fly. ______
d) If a number is prime, then it is odd. ______
e) If a figure has 4 sides, then it is a rectangle. ______
4) Write the converse of each statement. Tell whether the converse is true or false.
a) If a figure is a triangle, then it has three sides.
b) If it is raining, then the ground it wet.
c) If two angles form a linear pair, then they are adjacent.
5) Use the diagram and answer with PROPER notation.
a. Name a line. ______
b. Name 2 line segments. ______ ______
c. Name a ray with initial point B. ______
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d. Name 3 collinear points. ____ ____ ____
e. Name 3 noncollinear points ____ ____ ____
f. Name a point NOT on AC. ____
Sketch.
6) AB
7) CD
8) EF
9) two lines intersecting at point X
10) BE and BD so they are perpendicular.
11) three collinear points R, E, and D
13) Draw the next two figures in the pattern.
a.
b.
c.
12) three noncollinear points H, O, and T
Chapter 2: Segment Measures and Coordinate Graphs
Sketch a diagram for each situation described.
1. Points A, B, and D are collinear. Point A is 2. Points M, A, N, and Q are collinear. Point N is
between points B and D.
between points A and Q. Point M is not
between points A and Q.
In the diagram of collinear points, GK = 24, HJ = 10 , and GH = HI = IJ.
Label the diagram, and find the length of each segment.
3. HI = _______
4. IJ = _______
5. GH = _______
6. JK = _______
7. IG = _______
8. IK = _______
9. Sketch and label, then answer the question.
a) Points E, G, and O are collinear. E is between G and O.
If GE = 9 and EO = 10, then GO = _______
b) Points A, C, and T are collinear. A is between C and T.
If CT = 30 and CA = 12, then AT = _______
10. Use the diagram to answer the following questions.
a) What is the length of OS ? ______
b) What is the length of KN ? ______
c) Which segment is congruent to KL ? ______
d) Is M the midpoint of OK ? ______ (yes or no)
e) If P is the midpoint of which segment? ______
11) Use the coordinate plane to plot the points.
A(-2, 0)
B(4, -3)
C(0, 5)
D(-2, -7)
12) Use the number line to find the coordinate of the midpoint of each segment.
a) AL ______
b) KR _______
13) Find the midpoint of the segment.
(Hint: First write the coordinates of the endpoints).
a) SR
b) XU
Chapter 3: Angles
1) Use the diagram at the right. Name a pair of angles (remember 3 points!) that fit the
description.
a) vertical angles _________ and _________
E
b) supplementary angles _________and __________
c) complementary angles ________ and __________
D
d) linear pair _________ and _________
e) adjacent angles _________ and __________
B
C
F
A
2) What is the complement of a 57° angle? _______
3) What is the supplement of a 61º angle? _______
4) If one angle of a linear pair measures 102º, then the other measures ________.
5) If one vertical angle measures 39º, then the other measures ________.
6) x = _______
148º
7) y = ________
8) z = ________
38
xº
58º
yº
zº
61º
Use the diagram at the right to determine if each statement is true or false.
_______11. SR  PQ
_______12. NXP is a right angle.
_______13. QXP is a straight angle.
_______14. SXQ and PXR are vertical angles.
_______15. SXQ and QXN are a linear pair.
16. Name an angle tat forms a linear pair with SWU.
17. Name an angle that is adjacent to RWS.
18. Name an angle that is vertical to RWV.
19. mDAE = 25 and mCAD = 20. mCAE = _______
22. mBAD = 60 and mBAC = 35. m1 = _______