Download Lesson 2-6

Geometry
Chapter 2
Lesson 2-6
Example 1 Verify Algebraic Relationships
Solve 4(x + 3) = 52.
Algebraic Steps
4(x + 3) = 52
4x + 12 = 52
4x + 12 - 12 = 52 - 12
4x = 40
4x 40
= 4
4
x = 10
Properties
Original Equation
Distributive Property
Subtraction property
Substitution Property
Division Property
Substitution Property
Example 2 Write a Two-Column Proof
Write a two-column proof.
a. If 2(3x + 4) = 56, then x = 8
Statements
1. 2(3x + 4) = 56
2. 2(3x) + 2(4) = 56
3. 6x + 8 = 56
4. 6x + 8 – 8 = 56 – 8
5. 6x = 48
6.
6x 48
= 6
6
7. x = 8
Reasons
1. Given
2. Distributive Property
3. Substitution
4. Subtraction Property
5. Substitution
6. Division Property
7. Substitution
Geometry
Chapter 2
Example 3 Justify Geometric Relationships
Standardized Test Practice
If A  B, and B  C, then which of
the following is a valid conclusion?
I
II
III
mA = mB and mB = mC
A  C
A is complementary to C
A II only
C I, II and III
B I and II
D I and III
Read the Test Item
Determine whether the statements are true based on the given information.
Solve the Test Item
Statement I:
Examine the given information, A  B, and B  C. From the definition of congruent angles, if A
 B, and B  C, then mA = mB and mB = mC. Thus, Statement I
is true.
Statement II:
By the Transitive Property A  C. Thus, Statement II is true.
Statement III:
There is no information about the sum of the measures of the angles so there is no way to determine if
they are complementary. Thus, Statement III is not a valid conclusion.
Because Statements I and II are true, choice B is correct.
Example 4 Geometric Proof
TIME On a clock, the angle formed by the hands at 4:00 is a 120° angle. If the angle formed at 4:00
is congruent to the angle formed at 8:00, prove that the angle formed at 8:00 is a 120° angle.
Given:
m 4 = 120
4  8
Prove:
m8 = 120
Proof:
Statements
1. m 4 = 120
4  8
2. m4 = m8
3. 120 = m8
4. m8 = 120
Reasons
1. Given
2. Definition of congruent angles
3. Substitution
4. Symmetric Property