Download Geometry Review Worksheet

Geometry Review Worksheet
Chapter 2
Name:
Write yes or no to indicate whether you can assume
the information from the picture.
1. m<SQN = 90
2. <LOM and <MOQ are a linear pair.
3. Q is the midpoint of OR .
4. PR  OP
5. <PRQ and <SRT are vertical angles.
6. MO is less than PR.
7. P, O, and M are collinear.
8. <LOM  <SRT
9. . LQ is greater than LO
Complete the following proofs.
10.
Given: <2 and <5 are supplementary
Prove: <3 and <8 are supplementary
statements
1. <2 and <5 are supplementary
.
1.
2. m<2 + m<5 = 180
2.
3. <2  <3 and <5  <8
3.
4. m<3 + m<8 = 180
4.
5.
5.
reasons
.
11.
Given: m<2 = m<3
Prove: m<1 = m<4
(Proof completed on next page.)
(#13 continued)
statements
1. m<2 = m<3
.
1.
2. <1 and <2 are a linear pair
<3 and <4 are a linear pair
2.
3. m<1 + m<2 = 180
m<3 + m<4 = 180
3.
4. m<1 + m<2 = m<3 + m<4
4.
5. m<1 = m<4
5.
12.
.
reasons
.
reasons
.
Given: BD bisects AC ; AB  DC
Prove: AB  AD
statements
1. BD bisects AC ; AB  DC
.
1.
2. AD  DC
2.
3.
3.
13.
reasons
Given: <RXS and <RYS are right angles; <5  <6
Prove: <7  <8
statements
.
1. <RXS and <RYS are right angles; <5  <6
1.
2. <RXS  <RYS
2.
3. m<5 + m<7 = m<6 + m<8
3.
4. <7  <8
4.
14.
Given: BD bisects <CBE
Prove: <1 and <3 are supplementary
statements
1. BD bisects <CBE
.
reasons
1.
2. <2  <3
2.
3. <1 and <2 are a linear pair
3.
4.
4. The sum of the measures of the <’s
of a linear pair is 180.
5. m<1 + m<3 = 180
5.
6.
6.
15.
.
Given: 4(x + 5) + 1 = 2x - 1
Prove: x = -11
statements
.
reasons
1. 4(x + 5) + 1 = 2x - 1
1.
2. 4x + 20 + 1 = 2x - 1
2.
3. 4x + 21 = 2x – 1
3.
4. 2x + 21 = -1
4.
5. 2x = -22
5.
6. x = -11
6.
.
In 15-16, show each is false by providing a counterexample.
15. If it’s summer, then it must be July.
16. If two angles are congruent, then they are vertical. (Provide a sketch as a counterexample.)
17. If a conditional is true, which must be also be true? (More than one could apply.)
a) converse
b) inverse
c) contrapositive
d) biconditional
18. If the converse is true, which must be also be true? (More than one could apply.)
a) converse
b) inverse
c) contrapositive
d) biconditional
19. Write a conditional statement for the statement “I will take a nap if I’m tired.”
20. Consider the conditional “If a number is divisible by 10, then it is divisible by 5.”
a) Write the converse.
b) Write the inverse.
c) Write the contrapositive
d) Which of the above are true?
21. Combine the following two statements into a biconditional. Is the biconditional true?
If a number is divisible by 2, then it is even.
If a number is even, then it is divisible by 2.
Review problems from chapter 1. This will be on the test.
22. M is between N and O. NM = 17, MO = 3x -5, and NO = 5x + 2. Find NO.
(from Section 1-2)
23. KM bisects JKL, mJKM  4 x  6, and mMKL  7 x  12. Find mJKM .
(from Section 1-3)
24. A= (4, 7) and B = (-6, 2). Find the midpoint of AB . (from Section 1-6)
25. A= (4, 7) and B = (-6, 2). Find AB. (from Section 1-6)