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TEQ - Inequalities

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TEQ - Inequalities. Write out the theorem or postulate that allows the following conclusions (refer to picture at right). D. a). C. An exterior angle of a triangle is greater than either of its nonadjacent interior angles. B. A. b). A whole is greater than any of its parts. - PowerPoint PPT Presentation
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TEQ - Inequalities
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TEQ - Inequalities

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

HQAHMF ΔΔ .4 SASSAS .4

HH .3 3. Reflexive postulate

AQFM .5 5. CPCTC


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