2.6 2.6 Prove Statements about Segments and Angles Bell Thinger a property of equality to complete the statement. ANSWER AB = TU If AB = CD and CD = TU, then ? . f m 1 = m 3, then m 3 = ? . ANSWER RS; WX RS = WX, then ? + AB = ? + AB. ANSWER m 1
May 28, 2015
2.62.6 Prove Statements about Segments and Angles Bell Thinger
Use a property of equality to complete the statement.
ANSWER AB = TU
2. If AB = CD and CD = TU, then ? .
1. If m 1 = m 3, then m 3 = ? .
ANSWER RS; WX3. If RS = WX, then ? + AB = ? + AB.
ANSWER m 1
2.6
2.6Example 1Write a two-column proof for the situation in Example 4 from Lesson 2.5.
STATEMENTS REASONS
GIVEN:m∠ 1 = m∠ 3
PROVE:m∠ EBA = m DBC
1. Given1.m 1 = m 3
2.m EBA = m 3 + m 22. Angle Addition Postulate
3.m EBA = m 1 + m 23. Substitution Property of Equality
4.m 1 + m 2 = m DBC4. Angle Addition Postulate
5.m EBA = m DBC 5. Transitive Property of Equality
2.6Guided Practice
GIVEN : AC = AB + AB
PROVE : AB = BC
1. Four steps of a proof are shown. Give the reasons for the last two steps.
ANSWER
1. AC = AB + AB
2. AB + BC = AC
3. AB + AB = AB + BC
4. AB = BC
1. Given
2. Segment Addition Postulate
3. Transitive Property of Equality
4. Subtraction Property of Equality
STATEMENT REASONS
2.6
2.6Example 2
SOLUTION
Transitive Property of Angle Congruencea.
b. Symmetric Property of Segment Congruence
Name the property illustrated by the statement.
a. If R T and T P, then R P.
b. If NK BD , then BD NK .
2.6Guided Practice
Reflexive Property of CongruenceANSWER
Symmetric Property of CongruenceANSWER
Name the property illustrated by the statement.
2. CD CD
3. If Q V, then V Q.
2.6
GIVEN: M is the midpoint of AB .
Example 3
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.
b.AM = AB21
PROVE: a. AB = 2 AM
2.6
SOLUTION
1. M is the midpoint of AB. 1. Given
3. AM = MB 3. Definition of congruent segments
4. AM + MB = AB 4. Segment Addition Postulate
5. AM + AM = AB 5. Substitution Property of Equality
6. 2AM = ABa. 6. Simplify
AM = AB217.b. 7. Division Property of Equality
STATEMENTS REASONS
Example 3
2. AM MB 2. Definition of midpoint
2.6
2.6 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.
Shopping Mall
Example 4
2.6
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.
Example 4
2.6
GIVEN: B is the midpoint of AC .C is the midpoint of BD .
PROVE: AB = CD
STATEMENTS REASONS
1. B is the midpoint of AC .C is the midpoint of BD .
1. Given
2. Definition of midpoint2. AB BC
3. BC CD 3. Definition of midpoint
5. AB = CD
4. AB CD 4. Transitive Property of Congruence
5. Definition of congruent segments
Example 4
2.6Exit Slip
Reflexive Prop. Of Eq.2. ?
1. MA = TH ?
1. Copy and complete the proof.
GIVEN: MA = TH
PROVE: MT = AH
3. MA + AT = AT + TH ?
MA + AT = MT; AT + TH =AH4. ?
5. Substitution Prop. Of Eq. ?
STATEMENTS REASONS
2.
1.
3.
4.
5.
Given
AT = AT
Addition Prop. Of Eq.
Segment Add. Post.
MA + AT = MT; AT + MA=AH
GIVEN: MA = TH
PROVE: MT = AH
6. ? MT = AH Transitive Prop. Of Eq.6.
2.6Exit Slip2. Use the given information to
prove the statement.
PROVE: m 2 = 31o
GIVEN: m 1 + m 2 = 90 ;m 1 = 59
o
o
Statements (Reasons)ANSWER
(Subtraction Prop. Of Eq.)2. m 2 = 90 – m 1o
(Substitution Prop. Of Eq.)3. m 2 = 90 – 59o o
(Simplify)4. m 2 = 31o
(Given)1. m 1 + m 2 = 90 ; m 1 = 59 oo
2.6
Homework
Pg 117-120 #3, 7, 15, 17, 21