(8) Lesson 5.2 - Geometric Proof

1. Classify each pair of angles as alternate interior, alternate
exterior, or corresponding.
1. 1 and 8 2. 2 and 7 3. 1 and 3
Refer to the figure at the right. Line s is
perpendicular to line t. The measure
of 1 is 35°. Find each angle measure.
4. m2 5. m3
Course 3, Lesson 5-2

2. Course 3, Lesson 5-2
ANSWERS
1. alternate exterior
2. alternate interior
3. corresponding
4. 55°
5. 90°

3. HOW can algebraic concepts be
applied to geometry?
Geometry
Course 3, Lesson 5-2

4. Course 3, Lesson 5-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Geometry
• Preparation for 8.G.6
Explain a proof of the Pythagorean Theorem and its converse.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. To prove a conjecture
• using a paragraph proof,
• using a two-column proof
Course 3, Lesson 5-2
Geometry

6. • inductive reasoning
• deductive reasoning
• proof
• paragraph proof
• informal proof
• two-column proof
• formal proof
• theorem
Course 3, Lesson 5-2
Geometry

7. Course 3, Lesson 5-2
Geometry
Step 1 List the given information, or what you know. If
possible, draw a diagram to illustrate this
information.
Step 2 State what is to be proven.
Step 3 Create a deductive argument by forming a
logical chain of statements linking the given
information to what you are trying to prove.
Step 4 Justify each statement with a reason.
Reasons include definitions, algebraic
properties, and theorems.
Step 5 State what it is you have proven

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. The diamondback
rattlesnake has a
diamond pattern on its
back. An enlargement
of the skin is shown.
If m∠1 = m∠4, write a
paragraph proof to show
that m∠2 = m∠3.
Given: m∠1 = m∠4
Proof:
Prove: m∠2 = m∠3
m∠1 = m∠2 because they are vertical angles. Since m∠1 = m∠4,
m∠2 = m∠4 by substitution. m∠4 = m∠3 because they are vertical
angles. Since m∠2 = m∠4, then m∠2 = m∠3 also by substitution.
Therefore, m∠2 = m∠3.

9. Answer
Need Another Example?
Refer to the diagram. If
m∠1 = m∠5, write a paragraph
proof to show that m∠1 = m∠11.
m∠1 = m∠9 because they are corresponding
angles. m∠9 = m∠11 because they are vertical
angles. Since m∠9 = m∠11, then m∠1 = m∠11
by substitution.

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Write a two-column proof to show that if two
angles are vertical angles, then they have the
same measure.
Statements
lines m and n intersect;
∠1 and ∠3 are vertical angles.
Given: lines m and n intersect; ∠1 and ∠3 are vertical angles
Prove: m∠1 = m∠3
Reasons
a. Given
∠1 and ∠2 are a linear pair
and ∠3 and ∠2 are a linear pair.
b. Definition of linear pair
m∠1 + m∠2 = 180º
m∠3 + m∠2 = 180º
c. Definition of supplementary angles
m∠1 + m∠2 = m∠3 + m∠2d. Substitution
5 m∠1 = m∠3 Subtraction Property of Equalitye.

11. Answer
Need Another Example?
Write a two-column proof to show that if
PQ = QS and QS = ST, then PQ = ST.
Given: PQ = QS; QS = ST
Prove: PQ = ST
Statements
PQ = QS and QS = ST
Reasons
a. Given
PQ = STb. Substitution

12. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-2
Geometry

13. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-2
Geometry
Sample answers:
• When completing a two-column proof, you may define
a variable and write equations as part of the
statements.
• When completing a two-column proof, you use some
properties of equality for reasons.

14. Describe the differences
between a paragraph proof
and a two-column proof.
Ratios and Proportional RelationshipsFunctionsGeometry
Course 3, Lesson 5-2