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2-6
2-6 Geometric
GeometricProof
Proof
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Geometry
Holt
McDougal
Geometry
2-6 Geometric Proof
Warm Up
Determine whether each statement is true or
false. If false, give a counterexample.
1. It two angles are complementary, then they are
not congruent. false; 45° and 45°
2. If two angles are congruent to the same angle,
then they are congruent to each other. true
3. Supplementary angles are congruent.
false; 60° and 120°
Holt McDougal Geometry
2-6 Geometric Proof
Objectives
Write two-column proofs.
Prove geometric theorems by using
deductive reasoning.
Holt McDougal Geometry
2-6 Geometric Proof
Example 1: Writing Justifications
Write a justification for
each step, given that A
and B are supplementary
and mA = 45°.
1. A and B are supplementary.
mA = 45°
Given information
2. mA + mB = 180°
Def. of supp s
3. 45° + mB = 180°
Subst. Prop of =
Steps 1, 2
Subtr. Prop of =
4. mB = 135°
Holt McDougal Geometry
2-6 Geometric Proof
A theorem is any statement that you can
prove. Once you have proven a theorem, you
can use it as a reason in later proofs.
Holt McDougal Geometry
2-6 Geometric Proof
Holt McDougal Geometry
2-6 Geometric Proof
Holt McDougal Geometry
2-6 Geometric Proof
Holt McDougal Geometry
2-6 Geometric Proof
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Holt McDougal Geometry
2-6 Geometric Proof
Example 2: Completing a Two-Column Proof
Fill in the blanks to complete the two-column
proof.
Given: XY
Prove: XY  XY
Statements
1.
XY
2. XY = XY
3. XY
.

XY
Holt McDougal Geometry
Reasons
1. Given
2. Reflex.
.
Prop. of =
3. Def. of  segs.
2-6 Geometric Proof
Check It Out! Example 2
Fill in the blanks to complete a two-column proof of one
case of the Congruent Supplements Theorem.
Given: 1 and 2 are supplementary, and
2 and 3 are supplementary.
Prove: 1  3
Proof:
a. 1 and 2 are supp., and
2 and 3 are supp.
b. m1 + m2 = m2 + m3
c. Subtr. Prop. of =
d. 1  3
Holt McDougal Geometry
2-6 Geometric Proof
Example 3: Writing a Two-Column Proof from a Plan
Use the given plan to write a two-column proof.
Given: 1 and 2 are supplementary, and
1  3
Prove: 3 and 2 are supplementary.
Plan: Use the definitions of supplementary and congruent angles
and substitution to show that m3 + m2 = 180°. By the
definition of supplementary angles, 3 and 2 are supplementary.
Holt McDougal Geometry
2-6 Geometric Proof
Example 3 Continued
Statements
Reasons
1. 1 and 2 are supplementary. 1. Given
1  3
2. m1 + m2 = 180°
of supp. s
2. Def.
.
= m3
3. m1
.
3. Def. of  s
4. m3 + m2 = 180°
4. Subst.
5. 3 and 2 are supplementary 5. Def. of supp. s
Holt McDougal Geometry