Warm-Up Exercises
Use a property of equality to complete the statement.
1. If m
1=m
ANSWER
m
3, then m
3= ?
1
2. If AB = CD and CD = TU, then ?
ANSWER
.
AB = TU
.
Warm-Up Exercises
Use a property of equality to complete the statement.
3. If RS = WX, then
ANSWER
? + AB = ?
+ AB.
RS; WX
4. If m EFG = 28º and m GFH = 62º,
then ? + 62º = m EFG + m GFH.
ANSWER
28º
Warm-Up1Exercises
EXAMPLE
Write a two-column proof
Write a two-column proof for
the situation in Example 4
from Lesson 2.5.
GIVEN: m 1 = m 3
PROVE: m EBA = m DBC
STATEMENT
1.
2.
3.
4.
5.
REASONS
1.
m 1 = m 3
m EBA = m 3 + m 22.
m EBA = m 1 + m 23.
m 1 + m 2 = m DBC4.
m EBA = m DBC
5.
Given
Angle Addition Postulate
Substitution Property of Equality
Angle Addition Postulate
Transitive Property of Equality
Warm-Up
Exercises
GUIDED
PRACTICE
1.
for Example 1
Four steps of a proof are shown. Give the reasons
for the last two steps.
GIVEN : AC = AB + AB
PROVE : AB = BC
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 1
ANSWER
GIVEN : AC = AB + AB
PROVE : AB = BC
STATEMENT
REASONS
1. AC = AB + AB
1. Given
2. AB + BC = AC
2. Segment Addition Postulate
3. AB + AB = AB + BC
3. Transitive Property of Equality
4. AB = BC
4. Subtraction Property of Equality
Warm-Up2Exercises
EXAMPLE
Name the property shown
Name the property illustrated by the statement.
a. If
T and
R
b. If NK
T
BD , then BD
P, then
R
P.
NK .
SOLUTION
a. Transitive Property of Angle Congruence
b. Symmetric Property of Segment Congruence
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 2
Name the property illustrated by the statement.
2.
CD
CD
ANSWER
Reflexive Property of Congruence
3.
If
Q
V, then
V
Q.
ANSWER
Symmetric Property of Congruence
Warm-Up3Exercises
EXAMPLE
Use properties of equality
Prove this property of midpoints: If you know that M is
the midpoint of AB ,prove that AB is two times AM and
AM is one half of AB.
GIVEN: M is the midpoint of AB .
PROVE: a. AB = 2 AM
1
b. AM = 2 AB
Warm-Up3Exercises
EXAMPLE
Use properties of equality
STATEMENT
1. M is the midpoint of AB.
2. AM MB
3. AM = MB
4. AM + MB = AB
5. AM + AM = AB
a. 6. 2AM = AB
b. 7. AM = 1 AB
2
REASONS
1. Given
2.
3.
4.
5.
Definition of midpoint
Definition of congruent segments
Segment Addition Postulate
Substitution Property of Equality
6. Distributive Property
7. Division Property of Equality
Warm-Up
Exercises
GUIDED
PRACTICE
for Example 3
4. WHAT IF? Look back at Example 3. What would
be different if you were proving that AB = 2 MB
and that MB = 1 AB instead?
2
ANSWER
In step 5,6, and 7, AM would be replaced by MB
Warm-Up4Exercises
EXAMPLE
Solve a multi-step problem
Shopping Mall
Walking down a hallway at the mall, you notice the
music store is halfway between the food court and
the shoe store. The shoe store is halfway between the
music store and the bookstore. Prove that the
distance between the entrances of the food court and
music store is the same as the distance between the
entrances of the shoe store and bookstore.
Warm-Up4Exercises
EXAMPLE
Solve a multi-step problem
SOLUTION
STEP 1 Draw and label a diagram.
STEP 2 Draw separate diagrams to show mathematical
relationships.
STEP 3 State what is given and what is to be proved
for the situation.
Then write a proof.
Warm-Up4Exercises
EXAMPLE
Solve a multi-step problem
GIVEN: B is the midpoint of AC .
C is the midpoint of BD .
PROVE: AB = CD
STATEMENT
REASONS
1. B is the midpoint of AC . 1. Given
C is the midpoint of BD .
2. AB
BC
2. Definition of midpoint
3. BC
CD
3. Definition of midpoint
4. AB CD
5. AB = CD
4. Transitive Property of Congruence
5. Definition of congruent segments
Warm-Up
Exercises
GUIDED
PRACTICE
5.
for Example 4
In Example 4, does it matter what the
actual distances are in order to prove the
relationship between AB and CD? Explain.
ANSWER
No; Because the critical factor is the midpoint
6.
In Example 4, there is a clothing store halfway
between the music store and the shoe store. What
other two store entrances are the same distance
from the entrance of the clothing store?
ANSWER
Food Court and Bookstore
Daily
Homework
Quiz
Warm-Up
Exercises
1.
Copy and complete the proof.
GIVEN: MA = TH
PROVE: MT = AH
Statements (Reasons)
1. MA = TH
ANSWER
2.
?
( ? )
(Given)
(Reflexive Prop. Of Eq.)
ANSWER
AT = AT
Daily
Homework
Quiz
Warm-Up
Exercises
1.
Copy and complete the proof.
GIVEN: MA = TH
PROVE: MT = AH
Statements (Reasons)
3. MA + AT = AT + TH ( ? )
ANSWER
(Addition Prop. Of Eq.)
4. MA + AT = MT; AT + TH =AH ( ? )
ANSWER
Segment Add. Post.
Daily
Homework
Quiz
Warm-Up
Exercises
1.
Copy and complete the proof.
GIVEN: MA = TH
PROVE: MT = AH
Statements (Reasons)
5.
?
(Substitution Prop. Of Eq.)
ANSWER
MT = AH
Daily
Homework
Quiz
Warm-Up
Exercises
Use the given information to
prove the statement.
o
GIVEN: m 1 + m 2 = 90 ;
o
m 1 = 59
2.
PROVE: m
o
2 = 31
ANSWER
Statements (Reasons)
1. m
2. m
3. m
4. m
o
1 + m 2 = 90 ; m
o
2 = 90 – m 1
o
2 = 90o – 59
2 = 31o
o
(Given)
1 = 59
(Subtraction Prop. Of Eq.)
(Substitution Prop. Of Eq.)
(Simplify)