Download Section 2.6 Day 1 Proving Statements about Angles

Week 8
Warm Up
10.03.11
The following statement depicts which law of
deductive reasoning?
If it does not snow, then we will go camping.
If we go camping then we will cook marshmallows.
Geometry
2.6 Day 1
I will understand and use angle congruence
properties to prove statements.
Theorem 2.2
Properties of Angle Congruence
Reflexive
∠A ≅ ∠A
Symmetric
IF ∠ A ≅ ∠ B, then ∠B ≅ ∠A
Transitive
IF ∠A ≅ ∠B, and ∠B ≅ ∠C, then ∠A ≅ ∠C
Ex 1
Given: ∠ A ≅ ∠ B
Given: ∠ B ≅ ∠ C
B
C
A
Prove: ∠ A ≅ ∠ C
Step
Reason
∠A≅∠B
Given
∠B≅∠C
Given
m∠A = m∠B
Definition of congruent angles
m∠B = m∠C
Definition of congruent angles
m∠A = m∠C
∠A ≅ ∠C
Substitution property of equality
Definition of congruent angles
Ex 2
Given: m ∠ 3 = 40⁰
Given:
∠1 ≅ ∠2
Given:
∠2 ≅ ∠3
Prove: m ∠ 1 = 40⁰
Step
4
1
3
2
Reason
m ∠ 3 = 40⁰
Given
∠1 ≅ ∠2
Given
∠2 ≅ ∠3
Given
∠1 ≅ ∠3
m∠ 1 = m∠ 3
m ∠ 1 = 40⁰
Transitive property
of Equality
Definition of
congruent angles
Substitution property
of equality
Ex 2
Given: m ∠ 3 = 40⁰
Given:
∠1 ≅ ∠2
Given:
∠2 ≅ ∠3
Prove: m ∠ 1 = 40⁰
Step
m ∠ 3 = 40⁰
4
1
3
2
Reason
Given
∠1 ≅ ∠2
Given
∠2 ≅ ∠3
Given
∠1 ≅ ∠3
m∠ 1 = m∠ 3
m ∠ 1 = 40⁰
Transitive property
of Equality
Definition of
congruent angles
Substitution property
of equality
Right Angle Congruence
Theorem 2.3
All right angles are congruent.
B
A
Ex 3
Given:
∠ 1 and ∠ 2
are right angles
B
A
Prove: ∠ 1 ≅ ∠ 2
Step
Reason
∠ 1 and ∠ 2 are right angles
Given
m ∠ 1 = 90⁰
Definition of right angles
m ∠ 2 = 90⁰
Definition of right angles
m∠1 = m∠2
Substitution
property of equality
∠1 ≅
∠2
Definition of
congruent angles
Review
Do 1:
All right angles are ______________.
2
Given:
∠2 ≅ ∠3
Given:
∠3 ≅ ∠4
1
Given: m ∠ 2 = 25⁰
Prove: m ∠ 4 = 25⁰
Assignment:
Textbook Page 113, 10 – 17 all
and Page 125, 40 – 50 evens.
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