1 of 15

2.6 Proofs Using Segments

1

2 of 15

Supply the reason that supports each statement

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2

3 of 15

Complete the statement justified by the definition

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3

4 of 15

Supply the reason that supports each statement

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4

5 of 15

Supply each missing statement

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5

AB = CD; CD = EF

Given

_________________

Transitive property of equality

_________________

Given

FH = PQ

Symmetric property of equality

_________________

Given

JK = KL

Definition of congruent segments

_________________

Given

JK + KL = JL

Definition of between

6 of 15

Supply the missing statement or reason for each step (p 86 #22)

Given: AB = XY Prove: AX = BY

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6

A

X

B

Y

Statements

Reasons

AB = XY; A-X-B; X-B-Y

Given

______________________ and

______________________

Definition of between

AX + XB = XB + BY

______________________

______________________

Reflexive property of equality

AX = BY

______________________

7 of 15

Supply the missing statement or reason for each step (p 86 #23)

Given: lines l and k intersect at point P

Prove: Lines l and k lie in exactly one plane

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7

Statements

Reasons

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Given

Line l has at least one more point on it; call it M

Line k has at least one more point on it; call it N

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Plane postulate

Lines l and k lie in plane q

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k

l

P

8 of 15

Supply the missing statement or reason for each step (p 86 #24)

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8

Statements

Reasons

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Definition of congruent segments

AX + CX = BX + DX

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______________________;

______________________

Definition of between

AC = BD

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A

D

X

B

C

9 of 15

Draw a diagram and write a proof �(p 86 #26)

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9

10 of 15

Write a proof (p 86 #25)

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10

M

X

P

Q

L

11 of 15

Name the definition that justifies each statement

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11

12 of 15

Find each angle measure – give a reason why!

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12

13 of 15

Find all angles

13

1.

2.

3.

4.

14 of 15

Solve

  1. Find the coordinate of T if the coordinate of M, the midpoint of RT, is 2 and the coordinate of R is 5.
  2. Find the coordinate of the midpoint, B, of AC if A is located at -15 and C is located at 7. Verify the result with the length of each segment.
  3. Find the coordinate of the midpoints of FH, CE, and CG

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14

15 of 15

Find each angle

15

1.

2.