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TODAY IN GEOMETRY…
Warm Up Learning Goal 1: 2.6 You will
write proofs using geometric theorems
Independent Practice – 10 minutes! Learning Goal 2: 2.7 Use
properties of special pairs of angles
Ch. 2 Review
Ch.2 Test Wednesday/Thursday! Ch. 1 Retakes before
Wednesday/Thurs.!
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PROPERTIESREAL
NUMBERS SEGMENTS ANGLESREFLEXIVE
SYMMETRIC
TRANSITIVE
“equals itself”
“same in reverse”
“there’s a middle man”
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WARM UP: Use the property to copy and complete the statement.1. Substitute Property of Equality:
If , then .
2. Symmetric Property of Equality:If , then .
3. Addition Property of Equality:If , then
4. Transitive Property of Equality:If and , then
20𝐶𝐷
𝑚∠2𝑚∠1
𝐴𝐵 𝐶𝐷
𝑚∠1𝑚∠3
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TWO COLUMN PROOFS
using properties
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EXAMPLE: Four steps of a proof are shown. Give the reasons for the last two steps.
Statement
Reason
Given: Prove:
1. 1. Given.
2. 2. Segment Add’n Postulate
3. 3. ____________________
𝐴 𝐶𝐵
4. 4. ____________________
Transitive Property
Subtraction Property
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EXAMPLE: Four steps of a proof are shown. Give the reasons for the last two steps.
Statement
Reason
Given: , Prove:
1. , 1. Given.
2. 2. Segment Add’n Postulate
3. 3. ____________________
𝐴 𝐶𝐵
4. ___________________ 4. Simplify
Substitution Property
𝐴𝐶=11
5 6
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PRACTICE: Which property listed is the reason for the last step in the proof?
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10 minutesHOMEWORK #4:
Pg. 116: 5-11, 21 (Half sheet)
If finished, work on other assignments:
HW #1: Pg. 82: 3-18, 26-28, 47-54HW #2: Pg. 99: 3-8, 11-23HW #3: Pg. 109: 9-14
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MORE PRACTICEAngle Pair
Relationships
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PRACTICE:1. If
2. If
3. If
𝟏𝟏𝟐°𝟔𝟖°
𝟔𝟖°
𝟔𝟕°
𝟏𝟏𝟑°𝟏𝟏𝟑°
𝟕𝟏°𝟏𝟎𝟗°
𝟏𝟎𝟗°
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PRACTICE: Complete the statement with
a.
b.
c.
d. If , then
¿¿¿
¿
Both are right angles.
Vertical angles are congruent.
Angles 8 and 6 are complementary.
Angles 5 and 4 are a linear pair.
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PRACTICE: Find the values of x and y.
Vertical Angles are congruent!
Solve for x:
Solve for y:
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PRACTICE: Find the values of x and y.
Adjacent angles are linear pairs!
Solve for x:
3 𝑥+504 𝑥+322 𝑦
3 𝑦+30
Solve for y:
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HOMEWORK #5:
Pg. 127: 3-6, 8-11, 17-21, 28-29
If finished, work on other assignments:
HW #1: Pg. 82: 3-18, 26-28, 47-54HW #2: Pg. 99: 3-8, 11-23HW #3: Pg. 109: 9-14HW #4: Pg. 116: 5-11, 21 (in class work)