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Geometry
Final – 1st Semester (Chapters 1-6) – Part 1
Name ______________________
Use the diagram to name the figures. Be sure to use correct notation.
1. Three noncollinear points
2. Two opposite rays
3. One line segment
4. Three collinear points
5. Two rays which are not opposite rays
Find the distance between each pair of points. Show all work.
6. A(3,2), B(2,0)
7. E(-1,0), F(2,-4)
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Use the diagram to find the measure of the angle.
8. EAB
9. CAF
10. BAD
Classify the following angles (refer to the diagram for questions 8-10).
11. EAB
12. CAF
13. EAD
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BT bisects ABC . Find the value of x. Show all work and circle your final answer.
14.
15.
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Find the value of the variable. Show all work and circle your final answer.
16.
17.
Find the perimeter and area of each figure.
18.
19.
20.
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Write the inverse, converse, and contrapositive of the conditional statement.
21. If you like hockey, then you go to the hockey game.
Inverse:
Converse:
Contrapositive:
22. If x is odd, then 3x is odd.
Inverse:
Converse:
Contrapositive:
Using p and q below, write the symbolic statement in words.
p: The sky is cloudy.
q: It is raining.
23. : p
24. p  q
25. : q : p
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Match the statement with the Property of Equality.
A. Addition Property
B. Reflexive Property
C. Substitution Property
D. Transitive Property
E. Symmetric Property
F. Multiplication Property
G. Subtraction Property
26. _____ If JK  PQ and PQ  ST , then JK  ST .
27. _____ If mS  30o , then 5o  mS  35o
28. _____ If AB  CD  EF  CD , then AB  EF
29. _____ AB  AB
30. _____ If x  4 and y  x  5 , then y  9 .


31. _____ If mK  45o , then 3 mK  135o
32. _____ If mP  mQ , then mQ  mP .
Solve for the x using the given information. Show all work.
33. Given: GM  28
Use the diagram to decide whether the statement is true or false.
34. If m5  42o , then m6  48o .
35. If m5  42o , then m7  42o .
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Use the diagram to find the measure of the indicated angles.
36. mACD 
mACB 
Think of each segment in the diagram as part of a line. Fill in the blank with parallel,
skew, or perpendicular.
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37. WX and WT are _________________.
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38. RS and VW are _________________.
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39. TU and WX are _________________.
Complete the statement with corresponding, alternate interior, alternate exterior, or
same-side interior.
40. 6 and 10 are _______________ angles.
41. 7 and 9 are _______________ angles.
42. 8 and 9 are _______________ angles.
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Find the value of x. Be sure to show all your work.
43.
44.
Find the values of x and y. Be sure to show all your work.
45.
46.
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In questions 47-48, is it possible to prove that lines p and q are parallel? If so, give
the reason.
47.
48.
In exercises 49-50, use the diagram to state whether the given angles are
supplementary or congruent.
49. 2 and 6 are _______________________.
50. 3 and 5 are _______________________.
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Geometry
Final – 1st Semester (Chapters 1-6) – Part 2
Name ______________________
1. Find the slope of the line that passes through the points (3,-3) and (0,9).
The slopes of two lines are given. Are the lines parallel, perpendicular, or neither?
2. m1  3, m2 
1
3
2
5
3. m1   , m2 
5
2
Identify all triangles in the figure that fit the given description.
4. equilateral
5. scalene
6. obtuse
Find the value of x. Be sure to show all your work.
7.
8.
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Decide whether the figure is a polygon. Write ‘yes’ or ‘no’ next to each figure.
9.
10.
11.
Decide whether each statement is always, sometimes, or never true.
12. A rhombus is a square.
13. A rectangle is a parallelogram.
14. A trapezoid is a parallelogram.
15. Find the value of x.
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What special type of quadrilateral is shown?
16.
17.
18.
Find the value of x. Be sure to show all your work.
19.
20.
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21. List the 5 ways to prove triangles congruent.
Decide whether enough information is given to prove that the triangles are congruent. If
there is enough information, state the congruent postulate you would use.
22.
23.
24.
25.
26.
27.
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28. Complete the proof by supplying the reasons.
Given: AB  DC, AD  BC
Prove: A  C
Statement
Reason
AB  DC
AD  BC
BD  BD
ABD  CDB
A  C
29. Prove the following in the space provided.
Given: AC  AD
BC  BD
Prove: ACB  ADB
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Use the diagram to answer the following.
30. If RI  IT , which angles are congruent?
31. If TN  IT , which angles are congruent?
32. If 1  6 , which segments are congruent?
33. Use construction techniques with your compass and straightedge to copy the
segment below. Label the new segment GH , then construct the perpendicular
bisector to GH . Finally, label the midpoint of GH point M.
Find the indicated measure in each exercise.
34. The perpendicular bisectors of XYZ meet at
point P. Find PX.
35. The angle bisectors of XYZ meet at point P.
Find PM.
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In Exercises 37-39, complete the statement with the word always, sometimes, or never.
36. The perpendicular bisectors of a triangle will ____________________ intersect
on the triangle.
37. The angle bisectors of a triangle will ____________________ intersect outside
the triangle.
38. The medians of an acute triangle will ____________________ intersect inside the
triangle.
Use the figure shown and the given information.
L is the centroid of MNO , NP=11, ML=10, and NL=8.
39. Find the length of PO .
40. Find the length of MP .
41. Find the length of LQ .
42. Find the length of NQ .
In the diagram of XYZ where A, B, and C are the midpoints of the sides.
43. AB ____
44. If AC=3, then XZ= _____
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45. Find the perimeter of ABC given AX=2, XY=3, BC=9.
46. Find the value of x. Show all your work and circle your final answer.
47. List the sides in order from shortest to longest.
48. List the angles in order from smallest to largest.
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49. Using your compass, construct the angle bisectors to A,B, and C . Label the
intersection of the three angle bisectors point P. What is the special name for this
point?
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