Geometry Help!
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GeometryMidtermV2.128329.docxGeometry Midterm Exam
Name: ____________________________ Student Number: ____________________
Answer the questions below. Make sure to show your work and provide complete geometric explanations for full
credit.
1. Use the above figure to answer the following questions.
a. Name three points that are collinear
b. Name four coplanar points
c. What is the intersection of plane P and plane R?
d. Name a point that lies on both plane P and plane R
e. Name plane P and two more ways
2. To the nearest tenth, find the perimeter of ∆ABC with vertices A(2,4), B(-2,1) and C(2,1). Show your work.
3. Use the figure to complete each statement.
b. If AB = 10, then EB = _____
c. AE = ½ ______
d. ____ is the midpoint of _____
e. <BED = ______
4. If AB = 62, find the value of x. Show your work.
3x+16 2x-4
5. Write a conditional statement. Write the converse, inverse and contrapositve for your statement and determine the truth value of each. If a statement’s truth value is false, give a counterexample.
6. Name two pairs of congruent angles and justify your answer.
7. Write a two-column proof
Given: `
Prove: x = 45
8. Find the length of the third angle of a triangle given that the first two angles are 35 and 70. Show your work.
9. Write a congruency statement for the pair of triangles
10. Find the values of x and y. Show your work.
11. Which postulate or theorem, if any, could be used to prove the triangles congruent? If not enough information is given, write not enough information.
a.
b.
c.
d.
12. List the sides of each triangle from shortest to greatest
a.
b.
13. If AB is the midsegment, find the value of x. Show your work.
14. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.
15. In triangle ∆PQR, C is the centroid.
a. If CY = 10, find PC and PY
b. If QC = 10, find ZC and ZQ
c. If PX = 20, find PQ
16. For quadrilateral ABCD, determine the most precise name for it. A(2,3), B (12,3), C(8,6) and D(5,6). Show your work and explain.
17. For the parallelogram, find the value of the variables. Show your work.
5x + 2
3y – 6 24
12
18. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.
19. What is the sum of the measures of the exterior angles in a heptagon? Explain.
20. Find the measure of each interior angle and each exterior angles of the following regular polygons. Show your work.
a. Decagon
b. Pentagon
c. Dodecagon
d. 16-gon
e. 25-gon
