1. Algebraic Equations Setting up and Solving Equations for Basic Geometric Relationships

2. The Concept This Checkpoint requires students to be proficient on multiple previous Checkpoints. If you are having trouble with any of those concepts, please view those particular tutorials.

3. The Concept 1.For Each Question The First Thing You Must Do Is Identify The Relationship. 2.The Next Step Is To Use The Relationship To Setup An Equation. 3.Solve The Equation 4.Use The Answer To Complete The Problem.

4. Example 1 Identify the relationship: “Triangle Sum Theorem” - The 3 angles of a triangle have a sum of 180° 5x + 12° 3x - 20° 2x - 22° What is the measure of Angle A? A B C

5. Example 1 Setup an Equation: (5x + 12) + (3x – 20) + (2x – 22) = 180° 5x + 12° 3x - 20° 2x - 22° What is the measure of Angle A? A B C

6. Example 1 Solve the Equation: (5x + 12) + (3x – 20) + (2x – 22) = 180° 10x – 30 = 180° 10x = 210° 10x = 210° x = 21° x = 21° 5x + 12° 3x - 20° 2x - 22° What is the measure of Angle A? A B C

7. Example 1 Use The Answer To Complete The Problem SINCE x = 21°, then Angle A = 5x + 12° Angle A = 5(21°) + 12° Angle A = 105° + 12° Angle A = 117° 5x + 12° 3x - 20° 2x - 22° What is the measure of Angle A? A B C

8. Example 2 Identify the relationship: B & C are not related However, Angles A & C are corresponding angles and therefore are equal AND A & B are a straight angle pair and therefore have a sum of 180° 5x - 30° 3x + 10° What is the measure of Angle A? B C A

9. Example 2 Setup an Equation: m<A + m<B = 180° m<A = m<C m<C + m<B = 180° (3x + 10°) + (5x - 30°) = 180° 5x - 30° 3x + 10° What is the measure of Angle A? B C A

10. Example 2 Solve the Equation: (3x + 10°) + (5x - 30°) = 180° 8x - 20° = 180° 8x - 20° = 180° 8x = 200° 8x = 200° x = 25° x = 25° 5x - 30° 3x + 10° What is the measure of Angle A? B C A

11. Example 2 Use The Answer To Complete The Problem x = 25° m<A = m<C = 5x - 30° m<A = 5(25°) - 30° m<A = 125°- 30° = 95° 5x - 30° 3x + 10° What is the measure of Angle A? B C A