Download 3.2 Proof and Perpendicular Lines

Baird
Geometry
Updated: 10/13/03
3.2
Proof and Perpendicular Lines
GOAL: Write different types of proofs and prove results about perpendicular lines
VOCABULARY
A flow proof uses arrows to show the flow of the logical argument.
Theorem 3.1
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Theorem 3.2
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
Theorem 3.3
If two lines are perpendicular, then they intersect to form four right angles.
EXAMPLE 1: Different Types of Proofs
Write a two-column proof of Theorem 3.1.
Compare your proof to the flow proof
provided in Example 2 on page 137.
1
GIVEN:
∠1 ≅ ∠2, ∠1 and ∠2 are a linear pair
PROVE:
g⊥h
Statements
g
2
h
Reasons
1. ___________________________
1. ____________________________________________
2. ___________________________
2. ____________________________________________
3. ___________________________
3. ____________________________________________
4. ___________________________
4. ____________________________________________
5. ___________________________
5. ____________________________________________
6. ___________________________
6. ____________________________________________
7. ___________________________
7. ____________________________________________
8. ___________________________
8. ____________________________________________
9. ___________________________
9. ____________________________________________
10. __________________________
10. ____________________________________________
EXAMPLE 2: Different Types of Proofs
Write a paragraph proof of for the statement
below. This is part of the proof for Theorem 3.3.
Note that you are asked to complete a flow proof
of this theorem in problem 18 on p139.
GIVEN:
∠1 is a right angle
PROVE:
∠2 is a right angle
1
2
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EXAMPLE 3: Applications of the Theorems
Find the value of x. State the theorem that you are using.
a.
b.
xº
xº
xº
c.
d.
xº
2xº
xº