October 28, 2013
4.
2 supp 4
given
2= 3
m 2=m 3
= supp thm
3 supp 4
defn = angles
linear pr thm
8.
3 is a right angle
given
m 3 = 90
defn rt angle
3 supp 4
linear pr thm
m 3 + m 4 = 180
defn supp angles
90 + m 4 = 180
substitution property
m 4 = 90
subtraction property of =
A is a right angle
defn right angle
11.
13cm. Converse of Common Segs. Thm
12. 90o. If angles are congruent and supplementary, then they are right angles.
13. 37o. Vertical Angles Thm.
14. x = 2
15. y = 11
16. x = 8
October 28, 2013
Ch. 2 Study Guide
1. Be able to give the next item in a pattern.
2. Tell whether an argument uses inductive or deductive reasoning.
3. Write the converse, inverse, and contrapositive of a conditional statement and the truth
value of each.
4. Solve an algebraic equation and write a justification for each step.
5. For given statement, make a conclusion and supply a reason for that conclusion.
6. Complete two-column proofs by filling in missing statements and reasons.
7. Complete a flowproof by organizing the given statements in boxes and supplying
reasons.
8. Complete a logic puzzle.
9. Write a two-column proof.
October 28, 2013
1. Find the next item in the pattern.
-6, 12, -24, 48, ...
2. Inductive or Deductive?
a. All rectangles have 4 sides. A 4 sided figure is a quadrilateral. Figure
ABCD is a rectangle. Therefore, figure ABCD is a quadrilateral.
b. There has been frost on the ground when I wake up for the last 5 days.
Therefore there will be frost on the ground tomorrow when I wake up.
3. Write the converse, inverse, contrapositive and give the truth values.
Conditional: If a figure is a rhombus, then it is a quadrilateral. _____
Converse:
Inverse:
Contrapositive:
October 28, 2013
4.
A
8x+21
C
6x+5
B
4x-2
1. m ABC + m CBD = m ABD
D
1. ____________________
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5. Solve the equation. Write a justification for each step.
1. 5x - 3 = 4(x + 2)
1. _________________
October 28, 2013
6. Make a conclusion from each given and give a justification.
a. Given: AB = CD
Conclusion:
Reason:
b.
Given:
Conclusion:
2
1
Reason:
October 28, 2013
7. Fill in.
Given: m 1 = 63,
3 = 4
1= 3
Prove: m 4 = 63
Statement
Reason
1. ___________________ 1. given
2. ___________________ 2. given
3. ___________________ 3. ____________________
4. ___________________ 4. defn. = angles
5. m 1 = 63
5. given
6. ___________________ 6. ________________________
October 28, 2013
7. Complete the flowproof.
Given: AB = CD
A
B
C
Prove: AC = BD
1.
2.
Proof:
3.
4.
5.
AB = CD
CD + BC = AC
AC = BC
AB + BC = AC
BC + CD = BD
D
October 28, 2013
8. Proof.
Given: BC bis.
A
C
1
B
2
D
ABD
October 28, 2013