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Midterm
Basic Geometry
Midterm Review – Part 1
Date: _____________
Time: _____________
Vocabulary
acute angle
adjacent angles
angle
angle bisector
collinear
complementary
congruent
coplanar
degree
distance
exterior
interior
line
line segment
linear pair
midpoint
obtuse angle
perimeter
perpendicular
plane
point
ray
right angle
segment bisector
sides
supplementary
vertex
vertical angles
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. A(n) _________________ divides an angle into two congruent angles.
7. Two angles are _________________ if their measures have a sum of 180°.
8. Two angles that lie in the same plane are called _________________ if they share a
common side and a common vertex.
9. A(n) _________________ is an angle whose measure is less than 90°.
10. Two segments are _________________ if they have the same measure.
Sketch.
11) E, F, and G are noncollinear
points in plane R
12) AB bisects CD at P
14) BD bisects ABC
13) XY ||UV
Find the measure of the given angle.
15) m<ABE = _______
C
16) m<RQS = _______
R
D
A
E
53 21
S
P
63
m<PQS =
169º
Q
B
Use the information below to label the diagram and find the following:
17) If RS = 2x + 7, ST = 7x + 3, and RT = 19, find
a) x = ______
RS = _______
R

S
T
18) If P is the midpoint of AB, and AP = 4x + 3, and AB = 9x -9, find
a) x = ______
AB = ______

P
A
B
19) If PQ bisects RPT, and mRPQ = 3x + 7, and mQPT = 5x – 11, find
a) x = ______
mRPQ = ______
R
Q
T
P
Complete the following:
20) What is the complement of a 57° angle? _______
21) What is the supplement of a 61º angle? _______
22) If one angle of a linear pair measures 102º, then the other measures ________.
23) If one vertical angle measures 39º, then the other measures ________.
24) Find the value of x in each figure. (Use the Pythagorean Theorem)
a) x = ______
b) x = _______
c) x = _______
12
24
x
51
x
5
13
x
5
25) Plot the ordered pairs and find the length of each side segment.
A( -5, 2), B(3, 8) and C (3, 2)
a) length of AB _________
b) length of AC __________
c) length of BC __________
26) Plot the ordered pairs and find the length, midpoint, and slope of the segment.
C( -1, 7), D(2, -5) and E (2, 7)
a) length of CD _________
b) length of CE _________
c) length of DE _________
27) Find the length of PQ and the midpoint of PQ
P
Q


P
P
28) Use the diagram at the right. Name a pair of angles 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
Find the unknown angle measure.
29) x = _______
148º
30) y = ________
31) z = ________
38
xº
58º
yº
zº
32) Find the measure of each angle.
a)
m<1 = _____
b)
m<2 = _____
c)
m<3 = _____
1
2
3
42°
61º
Basic Geometry
Midterm Review – Part 2
1) Find the next two numbers in each sequence.
a) 3, 5, 9, 15, _____, _____
b) 3, 5, 9, 17, 33, _____, ______
c) 5, 1, -3, -7, _____, _____
2) Identify the hypothesis and conclusion of the following statement.
If the sum of 2 angles of a triangle is 90°, then the triangle is a right triangle.
Hypothesis: ______________________________________________
Conclusion: ______________________________________________
3) Tell whether each statement is true or false. If it is false, give a counterexample.
a) If a polygon is regular, then it is equilateral. ______
b) If 2 angles are supplementary, then they are congruent. ______
c) If all sides of a quadrilateral are congruent, then the figure is a square. ______
4) Write the converse of each statement. Tell whether the converse is true or false.
a) If a polygon is both equiangular and equilateral, then it is regular.
b) If ABC has an acute angle, then it is an acute triangle.
Basic Geometry
Midterm Review – Part 3
Important facts and formulas
Corresponding angles
If line f is parallel to line g then:
If two lines are perpendicular to the
same line, then they are parallel.
Ð1 and Ð5 , Ð3 and Ð7 ,
Ð2 and Ð6 , Ð4 and Ð8
Opposite interior angles Ð4 and Ð5,
Ð3 and Ð6
Opposite exterior angles Ð2 and Ð7 ,
Ð1 and Ð8
Same side interior angles Ð3 and Ð5 ,
Ð4 and Ð6
Same side exterior angles Ð1 and Ð7
Ð2 and Ð8
Corresponding angles are CONGRUENT.
Opposite interior angles are CONGRUENT.
Opposite exterior angles are CONGRUENT.
Same side interior angles are SUPPLEMENTARY.
Same side exterior angles are SUPPLEMENTARY.
If m ^ p and n ^ p, then m ||n
p
m
n
If two lines are parallel to the same line
then they are parallel
If m||p and n||p, then m||n
p
m
n
1) Identify each pair of angles.
a) Ð 1 and Ð 8 _____________________
b) Ð 4 and Ð 7 _____________________
c) Ð 3 and Ð 8 _____________________
d) Ð 4 and Ð 5 _____________________
e) Ð 2 and Ð 6 ____________________
1 3
2 4
5 7
6 8
2) Identify the type of angles. Find the value of x and the measure of each numbered
angle.
a) x = ______ m  1 = _______
m  2 = ________
b) x = _______
m  3 = _______
m  4 = _______
3
(7x - 4)°
(97 + 2x)°
1
2
(6x + 8)°
Type of angles______________
c) x = ______ m  5 = _______
m  6 = _______
5
138°
(3x + 6)°
6
Type of angles______________
(124 - x)°
4
Type of angles ___________________
d) x = _______ m  7 = _______
m  8 = _______
(2x + 3)° 7
(3x - 37)°
8
Type of angles ___________________
3. Set up an equation to solve for x.
a.
b.
5x-20
2x+26
c.
3x
(2x + 10)
d.
2x - 13
5x - 37
3x +3
3x + 17
2x
4. Use the figure to the right to find the values of x based upon the given information.
a. DCB = 90˚ and ECD = 3x + 24
b. If ray CA bisects DCE, find x if DCA = 3x – 16 and ACE = 7x – 42.
c. If ray CA bisects DCE, find x if ECD = 10x and ACE = 4x + 7˚.
d. BCD = 81˚, DCA = 3x – 12 and ACE = 6x – 48, what is x? What is DCA? What is
ACE?
11. Use the diagrams below to find the value of x in each of the following problems.
a. 1 = 131˚ and 3 = 13x + 1
c. 4 = 3x + 27 and 3 = 5x – 7
b. 7 = 13x and 6 = 4x + 10
d. 2 = 7x + 2y and 4 = 5x + 2y + 10
Pythagorean Theorem Review
For each of the following, find the missing/unknown side lengths.
1.
2.
x
15
20
24
3.
20
12
26
x
Midpoint and Distance Review
For each of the following, find the length of the specific segment and the midpoint of it
x