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Laabri

Geometry 2-5 Complete Lesson: Reasoning in Algebra and Geometry

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Last updated over 4 years ago
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2.

Take Note: Match each item on the left with the property it demonstrates on the right.

Assume that a, b, and c are real numbers, that a = b, and that c ≠ 0.

Draggable itemarrow_right_altCorresponding Item

If 7 = a, then a = 7.

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Addition Property of Equality

b = b

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Subtraction Property of Equality

a - 17 = b - 17

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Multiplication Property of Equality

5(a - b) = 5a - 5b

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Division Property of Equality

a ÷ 4 = b ÷ 4

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Reflexive Property of Equality

-3b = -3a

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Symmetric Property of Equality

a + 5 = b + 5

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Transitive Property of Equality

If a = b and b = 24, then a = 24.

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Substitution Property of Equality

If c = 10, then 10 can replace c in any expression.

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Distributive Property

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3.

Problem 1 Got It?

Given: ray AB bisects ∠RAN

What is the value of x? Justify each step.

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Take Note: Categorize each item on the left with the property it demonstrates on the right.

  • If \overline{PR} \cong \overline{TS} and \overline{TS} \cong \overline{ML}, then \overline{PR} \cong \overline{ML}.

  • \angle{1} \cong \angle{1}

  • If \angle{B} \cong \angle{M}, then \angle{M} \cong \angle{B}.

  • \overline{ST} \cong \overline{ST}

  • Reflexive Property of Congruence

  • Symmetric Property of Congruence

  • Transitive Property of Congruence

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5.

Problem 2 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 3 Got It? Complete the two-column proof on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

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Problem 3 Got It? Reasoning: In Problem 3, why is Statement 2 necessary in the proof?

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17.

Review Lesson 2-4: Use logical reasoning to draw a conclusion. State your conclusion in the response field.

If a student is having difficulty in class, then that student's teacher is concerned.

Walt is having difficulty in science class.

On the canvas, circle the law that justifies your conclusion.

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18.

Review Lesson 1-4: Use the diagram to identify the measure of each angle in the right column below.

Some measurements will not be used.

  • 10

  • 70

  • 45

  • 80

  • 125

  • 65

  • 90

  • m\angle{AOC}

  • m\angle{DOB}

  • m\angle{AOD}

  • m\angle{BOE}

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19.

Review Lesson 1-5: Find the value of the variable. Enter only a number.

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Review Lesson 1-5: Find the value of the variable. Enter only a number.

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Review Lesson 1-5: Find the value of the variable. Enter only a number.

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Review Lesson 1-5: Find the value of the variable. Enter only a number.

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Vocabulary Review: Classify each item on the left.

  • 5+3^4

  • 2(a-5)^2

  • 9<x-2

  • 3x+2=4

  • Equation

  • Not and equation

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24.

Use Your Vocabulary: Match each equation in the left column with the property you would use to justify it on the right.

Draggable itemarrow_right_altCorresponding Item

2\cdot (5\cdot x)=(2 \cdot 5) \cdot x

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Commutative Property of Addition

3+7=7+3

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Commutative Property of Multiplication

1+(9+53)=(1+9)+53

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Associative Property of Multiplication

12(4)=4(12)

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Associative Property of Addition

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Reflection: Math Success

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