# Chapter 2: Geometric Reasoning: Section 2.5: Algebraic Proofs

```Geometry B
Name:_____________________
Date: ____________
Block: ________
Chapter 2: Geometric Reasoning: Section 2.5: Algebraic Proofs
1) Amy’s favorite breakfast cereal has 102 Calories per serving. The equation C = 9f + 90
relates the grams of fat f in one serving to the Calories C in one serving. How many grams
of fat are in one serving of the cereal? Solve the equation for f and justify each step.
2) The equation C = \$5.75 + \$0.89m relates the number of movie rentals m to the monthly
cost C of a movie club membership. How many movies did Elias rent this month if his
membership cost \$11.98? Solve the equation for m and justify each step.
3) Identify the property that justifies each statement.
m∠1 = m∠2, and m∠2 = m∠4. So m∠1 = m∠4
x = y, so y = x
AB ≅ AB
ST ≅ YZ, and YZ ≅ PR. So, ST ≅ PR.
4) Solve each equation. Write a justification for each step.
y+1=5
0 = 2 (r - 3) + 4
Geometry B
5) Use the indicated property to complete each statement.
Reflexive Property of Equality: 3x - 1 = ______________
Transitive Property of Congruence: If ∠ A ≅ ∠ X and ∠ X ≅ ∠T, then _______________
Symmetric Property of Congruence: If BC ≅NP, then __________________
6) Solve each equation. Write a justification for each step.
5x - 3 = 4 (x + 2)
9y + 17 = -19
- (h + 3) = 72
- 2 = -10
7) Write a justification for each step.
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