Download Geometry Midterm Exam

Geometry Midterm Exam
Score: ______ / ______
Taziah clark
Name: _____________________________
: JM1308396
Student Number: ____________________
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.
7in
A. __________
5in
B. __________
9in
C. __________
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Geometry Midterm Exam
2 Name four rays shown.
ray xz, ray yz, ray xy and ray vz.
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.
39+41 = 80 and 80/2 = 40
(-84 + -120)/2 = -204/2 = -102
so it would be 40n and -102w
4 Write the conditional statement that the Venn diagram illustrates.
if closed figures is squares then closed figures is quadrilaterals.
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.
This is false becuase if it is snowing in one state does not mean it is
snowing in the rest of the states now if u said, if it is snowing in san antonio texas than it is
snowing at seaworld. This would be an accrate statment.
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Geometry Midterm Exam
6 What is the value of x? Justify each step.
AB + BC = AC
segment addition postulate
a.__________________________
2x + 6x + 8 = 32
substitution
b. __________________________
8x + 8 = 32
Simplification
c. __________________________
8x = 24
d. __________________________
X=3
e. __________________________
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Addition property of equality
Multiplication property of equality
Geometry Midterm Exam
7 Give the missing reasons in this proof of the Alternate Interior Angles Theorem.
Given:
Prove:
Corresponding Angles Postulate
a. ________________________
veritcally opposite angles
b. ________________________
alternate intereir angles
c. ________________________
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Based on the given information, can you conclude that ∆𝑄𝑅𝑆 ≅ ∆𝑇𝑈𝑉 ? Explain.
Given: ̅̅̅̅
𝑸𝑹 ≅ ̅̅̅̅
𝑻𝑼, ̅̅̅̅
𝑸𝑺 ≅ ̅̅̅̅
𝑻𝑽,
and ∆𝑄𝑅𝑆 ≅ ∆𝑇𝑈𝑉
They are congruent by sas.
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Geometry Midterm Exam
9 Write the missing reasons to complete the proof.
Given:
Prove:
,
, and
Statement
Reason
1.
2.
1. Given
3.
3. Given
2. Given
4. Definition of congruent
segments
5. ?
6. Segment Addition Postulate
7. Definition of congruent
segments
8. ?
4.
5.
6.
7.
8.
"Addition property of equality.
Step 5: _______________
sas
Step 8: _______________
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Geometry Midterm Exam
10 Fill in the missing reasons to complete the proof.
Given:
Prove:
Statement
1.
Reason
1. Given
2. Converse of the Corresponding Angles
Postulate
2.
3.
4.
5.
3. ?
4. Given
5. Transitive Property
6. ?
6.
property of congruent triangles
Step 3: ________________
isosceles triangle
Step 6: ________________
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Geometry Midterm Exam
11 Is
by HL? If so, name the legs that allow the use of HL.
yes bd.
12 Complete the proof by providing the missing reasons.
Given:
Prove:
,
Statement
1.
Reason
,
2.
angles
3.
, and
are right
1. Given
2. Definition of perpendicular
segments
3. ?
4. ?
4.
5.
5. ?
perpendicular segments
Step 3: ____________________
perpendicular segments
Step 4: ____________________
perpendicular segments
Step 5: ____________________
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Geometry Midterm Exam
13 Write a paragraph proof to show that
Given:
.
and
they are congruent triangles using SAS. they give two sides that are equal and using
the rule of intersecting lines I can show that the sharing angles are equal.
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Given:
is the perpendicular bisector of IK. Name two lengths that are equal.
ak and bi.
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Geometry Midterm Exam
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.
she went forward 6 then went 16 backwards witch would be -10 then she went 8 forward
witch will put her at -2.so she will not be at the same place she started at.
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.
Each triangle has three midsegments and
each is parallel to the third side. So by joining
the midpoints you are cutting the triangle in
equal parts.
17 Judging by appearance, classify the figure in as many ways as possible using rectangle, square,
quadrilateral, parallelogram, rhombus.
parrallelogram, rhombus
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Geometry Midterm Exam
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. 360
b. 180-360\n
c.
360
360\n
d.
e.
180
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Becuase the both are in a straight line.
Geometry Midterm Exam
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?
isosceles trapezoid.
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.
the point C will be on the x-axis at say (-x1,0). point D will be an equal distance
from the origin, but at (+x1,0) The perpendicular bisector of segment CD will go
through the mid-point (0,0), and be 90º to the x-axis.
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