Geometry Essentials
NOTES: Section 2.6: Algebraic Proofs
Name ____________________________________
Bonus Example: State the property that justifies each statement.
𝑥
1. If = 3, then x = 12
2. If m3 = 10 and m3 = m4, then m4 = 10
3. 𝑇𝑀 ≅ 𝑇𝑀
4. If OB = BG and BG = ED, then OB = ED
5. If m7 – 44 = 56, then m7 = 100
6. If 4 = x, then x = 4.
4
Algebraic Proof: a proof that is made up of a series of algebraic statements.
The properties of equality provide justification for many statements in algebraic proofs.
Example 1a:
Given: 12x – 9 = 4x + 39
Prove: x = 6
1.
1.
2.
2.
3.
3.
4.
4.
Example 1b:
Given: 2(5 – 3a) – 4(a + 7) = 92
Prove: a = –11
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
Example 2: If the distance d an object travels is given by d = 20t + 5, the time t that the object travels is given by t =
column proof to verify this conjecture.
Given: d = 20t + 5
𝑑−5
Prove: t =
20
Statements
Reasons
1. d = 20t + 5
1.
2. d – 5 = 20t
2.
3.
3. Division Property
4. t =
𝑑−5
4.
20
Example 3:
Given:
Prove: RS = 12
Statements
Reasons
1.
1. Given
2.
2. Given
3.
3. _________________
4. AB = RS
4. Definition of congruent segments
5. AB = 12
5. Given
6. RS = 12
6. Substitution
𝑑−5
20
. Write a two-
Geometry
Section 2.6 Day 1 Homework Worksheet
Name: _____________________________________
State the property that justifies each statement.
1. If 80 = m∠A, then m∠A = 80.
2. If RS = TU and TU = YP, then RS = YP.
3. If 7x = 28, then x = 4.
4. If VR + TY = EN + TY, then VR = EN.
5. If m∠1 = 30 and m∠1 = m∠2, then m∠2 = 30.
Complete the following proof.
6. Given: 8x – 5 = 2x + 1
Prove: x = 1
Proof:
Statements
Reasons
1. 8x – 5 = 2x + 1
1.________________________
2. 6x – 5 = 1
2.________________________
3. Addition Property
3. ______________
4. ______________________
4. x = 1
7. William’s father is eight years older than 4 times William’s age. William’s father is 36 years old.
a. Let x be William’s age. Translate the given information into an algebraic equation involving x.
b. Fill in the missing steps and justifications for each step in finding the value of x.
Statements
Properties
1. 4x + 8 = 36
1.
2.______________
2. Subtraction property
3. x = 7
3. _______________