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CABD
ADCADB
A B C
D
1.Write out the theorem or postulate that allows the following conclusions (refer to picture at right).
a)
b)
2. Write out the reason for the following conclusions.a) if A < B and C = D, then A + C < B + D
When equal quantities are added to unequal quantities, their sum is unequal in the same order
b) if A < B and B < D, then A < D
Transitive postulate of inequalities
c) if A < B and C = D, then A - C < B - D
Subtraction posulate of inequalities
An exterior angle of a triangle is greater than either of its nonadjacent interior angles
A whole is greater than any of its parts
ABAD
BCDC
ABAD .1
BCDC .2
AEBAED
E
A
D
C
B
Given:
Prove:
Statement Reason
1. Given
TEQ #3
2. Given
ACAC .3 3. Reflexive postulate
ABCADC ΔΔ .4 SSSSSS .4
AEBAED .8
21 .5
8. CPCTC
ABEADE ΔΔ .7 SASSAS .7 AEAE .6 6. Reflexive postulate
5. CPCTC
AFAE
ADAB
ABAE2
1
ADAF2
1
B
D
E
F
CBased on the diagram, prove:
Statements Reasons
1. 1. GIVEN
2.
3.
2. GIVEN
3. GIVEN
ADAB2
1
2
1 .4 4. Multiplication postulate of
inequalities
AFAE .5 5. Substitution postulate of inequalities
5.
A
Statement Reason
1. GivenADAB 1.
2. GivenDEBC 2.
3. When equal quantities are added to unequal quantities, their sum is unequal in the same order
DEADBCAB 3.
4. Partition postulate
AEDEADACBCAB
4.
5. Substitution postulate of inequalities
AEAC 5.
B
C
D
E
A
6.
Statement Reason
CBCA 1.
CBACAB .3 3. Angles opposite congruent sides of a triangle are congruent
4. Substitution PostulateCBAECB .4
CABECB 2.
1. Given
2. Given
ABCE .5 5. Two lines cut by a transversal that form congruent alternate interior angles are parallelAB
CE
ABCE //Based on the diagram, prove:
7.
D
8) Which of the following statements must be true?
a) 314 mmm
321 mmm
214 mmm
341 mmm
14 mm
41 mm
34 mm
43 mm
1 3 4
Questions 8 & 9 are based on the diagram above.
b)
c)
d)
9) Which of the following statements must be true?
a)
b)
c)
d)
2
Statement Reason
1. Given2 1. B
B1 2. 2. An exterior angle of a triangle is greater than either of its nonadjacent interior angles
3. Transitive postulate of inequalities
21 3.
B D C1
2
21 :Prove
11. A
1. Given
2. Given
CBAB 1.
CDBADB ΔΔ .6 SSSSSS .6
ACD of
midpoint theis .3 3. A median extends from a vertex of a triangle to the midpoint of the opposite side
ACBD
tomedian a is 2.
DBDB .5 5. Reflexive postulate
CDBADB .7
BDAC .8 8. Two intersecting lines that form congruent adjacent angles are perpendicular
DCAD .4 4. A midpoint divides a segment into 2 congruent parts
7. CPCTC
12.
1. Given
2. Given
ACBD 1.
CDBADB ΔΔ .7 SASSAS .7
AC D ofmidpoint theis 2.
DBDB .6 6. Reflexive postulate
CA .8 8. CPCTC
DCAD .5 5. A midpoint divides a segment into 2 congruent parts
anglesright are 2 and 1 3.
21 4.
3. Perpendicular lines form right angles
4. All right angles are congruent