Geometry Midterm Exam
Score: ______ / ______
Name: Don Palmer
Student Number: JM0328655
Directions: Answer each question in the space below the question. Show your work when applicable.
1 Label the net for the figure below with its dimensions.
A. 5 in.
B. 7 in.
C. 9 in.
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Geometry Midterm Exam
2 Name four rays shown.
   
VX XY YZ XZ
3 You live in Carson City, Nevada, which has approximate (latitude, longitude) coordinates of
(39N, 120W). Your friend lives in Ottawa, Ohio, with coordinates of (41N, 84W). You plan to meet
halfway between the two cities. Find the coordinates of the halfway point.
N  (39 + 41) / 2 = 40 N
W  ( 120 + 84) / 2 = 102 W
4 Write the conditional statement that the Venn diagram illustrates.
If a figure is a quadrilateral, then it’s a square.
If a figure is a square, then it’s a quadrilateral.
5 Is the following conditional true or false? If it is true, explain why. If it is false, give a
counterexample.
If it is snowing in Dallas, Texas, then it is snowing in the United States.
True – Because Dallas, Texas is in United States
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Geometry Midterm Exam
6 What is the value of x? Justify each step.
AB + BC = AC
a. Add & definition of between
2x + 6x + 8 = 32
b. Sub with given info
8x + 8 = 32
c. Simplifying 2x + 6x = x(2 + 6) = 8x
8x = 24
d. Sub property of equality (-) 8 both sides
X=3
e. Div prop of equality (multiplicative inverse prop) div by 8 on both sides)
7 Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given:
Prove:
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Geometry Midterm Exam
a. Definition of congruent angles
b. Vertical angles
c. Alternate interior angles
8 Based on the given information, can you conclude that
Given:
,
Yes, they are congruent
2 sides and included angle are equal
4
and
? Explain.
Geometry Midterm Exam
9 Write the missing reasons to complete the proof.
Given:
,
, and
Prove:
Statement
1.
2.
3.
4.
5.
6.
7.
8.
Reason
1. Given
2. Given
3. Given
4. Definition of congruent
segments
5. ?
6. Segment Addition Postulate
7. Definition of congruent
segments
8. ?
Step 5: Add. Prop of equality
Step 8: Congruent triangles
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Geometry Midterm Exam
10 Fill in the missing reasons to complete the proof.
Given:
Prove:
Statement
1.
2.
3.
4.
5.
6.
Step 3: Transversals
Step 6: Isosceles
6
Reason
1. Given
2. Converse of the Corresponding Angles
Postulate
3. ?
4. Given
5. Transitive Property
6. ?
Geometry Midterm Exam
11 Is
by HL? If so, name the legs that allow the use of HL.
BD is the leg & AD/CD are the respective hypotenuse
12 Complete the proof by providing the missing reasons.
Given:
Prove:
Statement
1.
,
2.
angles
3.
4.
5.
,
Reason
, and
are right
1. Given
2. Definition of perpendicular
segments
3. ?
4. ?
5. ?
Step 3: Perpendicular segments
Step 4: Reflexive Property of Congruence
Step 5: Hypotenuse Leg Theorem
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Geometry Midterm Exam
13 Write a paragraph proof to show that
Given:
and
.
AC is congruent to DC & BC is congruent CE because that’s given. The figure can conclude that
angles ACB & DCE are equal because they are vertical angles & therefore congruent. Then state that
triangles ABC and triangle DEC are congruent from SAS.
14 Given:
is the perpendicular bisector of IK. Name two lengths that are equal.
The equal lengths are IJ & JK – bisecting means to cut into 2 equal parts.
15 Li went for a mountain-bike ride in a relatively flat wooded area. She rode for 6 km in one direction
and then turned and pedaled 16 km in another. Finally she turned in the direction of her starting
point and rode 8 km. When she stopped, was it possible that Li was back at her starting point?
Explain.
No, it’s not possible. Li is about 2km short of the starting point. Explain: She rides 6km in one
direction, means she 6km from the starting point. When she turns & pedals 16km in another
direction heading back to the starting point. 16km – 10km = 2k
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Geometry Midterm Exam
16 Mei has a large triangular stone that she wants to divide into four smaller triangular stepping stones
in a pathway. Explain why cutting along each midsegment creates four congruent stepping stones.
They are congruent because of the mid-segment theorem. The triangles all have the same sides,
therefore, the triangles are congruent to one another.
17 Judging by appearance, classify the figure in as many ways as possible using rectangle, square,
quadrilateral, parallelogram, rhombus.
Parallelogram and Rhombus
18 For a regular n-gon:
a. What is the sum of the measures of its angles?
b. What is the measure of each angle?
c. What is the sum of the measures of its exterior angles, one at each vertex?
d. What is the measure of each exterior angle?
e. Find the sum of your answers to parts b and d. Explain why this sum makes sense.
a. 180*(n-2) = (2n-4) *90
b. 180 – 360 /n
c. 360 (for all n sided polygons)
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Geometry Midterm Exam
d. 360 /n
e. 180
19 Find the midpoint of each side of the trapezoid. Connect the midpoints. What is the most precise
classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid?
AB = 2
BC = sqrt 20
CD = 6
AD = sqrt 20
The quadrilateral formed by joining the midpoints of the sides of the trapezoid is a rhombus
because it has all 4 sides congruent.
20 Prove using coordinate geometry: If a point is on the perpendicular bisector of a segment, then it is
equidistant from the endpoints of the segment.
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Geometry Midterm Exam
Given: Line l is the perpendicular bisector of
.
Prove: Point R(a, b) is equidistant from points C and D.
Pythagoras theorem
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