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Warm-Up

Warm-Up. If the measure of an angle is 78° less than the measure of its complement, what is the measure of the angle? 6 12 51 84 (hint….let x= the measure of the unknown angle). 3.1: Properties of Parallel Lines. Objectives: Identify angles formed by two lines and a transversal

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Warm-Up

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  1. Warm-Up If the measure of an angle is 78° less than the measure of its complement, what is the measure of the angle? • 6 • 12 • 51 • 84 (hint….let x=the measure of the unknown angle)

  2. 3.1: Properties of Parallel Lines Objectives: Identify angles formed by two lines and a transversal Prove and use properties of parallel lines

  3. TRANSVERSAL: • Line intersects 2 coplanar lines in 2 distinct points • The intersection of a transversal and the 2 lines form 8 angles Transversal n intersects line l and m

  4. The angles formed when a transversal intersects 2 lines depends on their position ALTERNATE INTERIOR ANGLES: • Non-adjacent • Lie on opposite sides of the transversal in between the 2 lines it intersects

  5. Same-Side Interior Angles (Co-interior) • Lie on the same side of the transversal between the two lines

  6. Alternate Exterior Angles • Lie outside the 2 lines on opposite sides of the transversal

  7. Same-Side Exterior Angles • Lie outside the 2 lines on same side of transversal

  8. Corresponding Angles • Lie on the same side of the transversal • In corresponding positions

  9. If a transversal intersects 2 parallel lines: • Corresponding angles are congruent • Alternate interior angles are congruent • Same side interior angles are supplementary

  10. Finding Measures of Angles a b c d Find the measure of each angle. Justify your answer. 8 7 6 2 50° 5 4 1 3

  11. Find the values of x and y. Then find the measures of the angles. (2x)° y° (y-50)°

  12. Using Algebra to Find Angle Measures Find x and y. What do we know?? 50° y° x° 70°

  13. Two-Column Proof • Displays steps that prove a statement • Statements on left; Reasons/justifications on right • Use theorems, postulates, definition, properties and given statements for justifications GIVEN: (what you know) PROVE: (what you must show) Statements:Reasons: 1. 1. 2. 2. 3. 3. . . . . . .

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