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.- 5 in.
- 7 in.
- 9 in.
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
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:
- Definition of congruent angles
- Vertical angles
- Alternate interior angles
8 / Based on the given information, can you conclude that ? Explain.
Given: ,and
Yes, they are congruent
2 sides and included angle are equal
9 / Write the missing reasons to complete the proof.
Given: , , and
Prove:
Statement / Reason
1. / 1. Given
2. / 2. Given
3. / 3. Given
4. / 4. Definition of congruent segments
5. / 5. ?
6. / 6. Segment Addition Postulate
7. / 7. Definition of congruent segments
8. / 8. ?
Step 5: Add. Prop of equality
Step 8: Congruent triangles
10 / Fill in the missing reasons to complete the proof.
Given:
Prove:
Statement / Reason
1. / 1. Given
2. / 2. Converse of the Corresponding Angles Postulate
3. / 3. ?
4. / 4. Given
5. / 5. Transitive Property
6. / 6. ?
Step 3: Transversals
Step 6: Isosceles
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 / Reason
1. , , and / 1. Given
2. are right angles / 2. Definition of perpendicular segments
3. / 3. ?
4. / 4. ?
5. / 5. ?
Step 3: Perpendicular segments
Step 4: Reflexive Property of Congruence
Step 5: Hypotenuse Leg Theorem
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
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)
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.
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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