Parallel and Perpendicular Lines Geometry – Chapter 3
Chapter 3 Standards 2.0 Students write geometric proofs 4.0 Students prove basic theorems involving congruence 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal 12.0 Students find and use measures of interior and exterior angles of triangles and polygons to classify figures and solve problems.
3.1 Properties of Parallel Lines EQ: Identify different types of angles formed by parallel lines. a transversal is a line that intersects two coplanar lines at two distinct points. the diagram shows the eight angles formed by a transversal t and two lines, l and m.
3.1 Properties of Parallel Lines EQ: Identify different types of angles formed by parallel lines. There are special names for certain angles in a 2 line and transversal relationship alternate interior angles same-side interior angles corresponding angles alternate exterior angles same-side exterior angles Draw a transversal using a ruler through your not-parallel lines. Discuss which angles you think are which and why.
3.1 Properties of Parallel Lines EQ: Identify different types of angles formed by parallel lines. alternate interior angles same-side interior angles corresponding angles alternate exterior angles same-side exterior angles
3.1 Properties of Parallel Lines EQ: Identify different types of angles formed by parallel lines. Draw a transversal using a ruler through your parallel lines. Use a protractor to measure all of the angles. Discuss and draw conclusions about angle relationships when the two lines are parallel. alternate interior angles same-side interior angles corresponding angles alternate exterior angles same-side exterior angles
3.1 Properties of Parallel Lines EQ: Identify different types of angles formed by parallel lines.
3.1 Properties of Parallel Lines EQ: Identify different types of angles formed by parallel lines. Homework: page 132 (1-16) all
3.2Proving Lines Parallel EQ: Prove the converses to the theorems of section 3.1 What is the Corresponding Angles Postulate? What is the converse to this?
3.2Proving Lines Parallel EQ: Prove the converses to the theorems of section 3.1 Everything goes back to either the Corresponding Angles Theorem or the Converse of the Corresponding Angles Theorem. When you begin a proof involving parallel lines, you should ask yourself “How do I show that corresponding angles are congruent?”
3.2Proving Lines Parallel EQ: Prove the converses to the theorems of section 3.1 What is the converse to the Alternate Interior Angles Theorem? If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. Proof:
3.2Proving Lines Parallel EQ: Prove the converses to the theorems of section 3.1 What is the converse to the Same-side Interior Angles Theorem? If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. Proof:
3.2Proving Lines Parallel EQ: Prove the converses to the theorems of section 3.1 State the Converse to the Alternate Exterior Angle Theorem If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel. Proof:
3.2Proving Lines Parallel EQ: Prove the converses to the theorems of section 3.1 State the Converse to the Same-side Exterior Angle Theorem If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel. Proof:
3-3 Parallel and Perpendicular Lines EQ: Use previously proven theorems to prove theorems about parallel and perpendicular lines.
Homework: page 137 (1-21) all page 143 (1-3)
Warm Up In this drawing, line k is parallel to line j Which angle is alternate interior with ∠4? Which angle is corresponding to ∠8? m∠3 = 37. What is m∠6? m∠1 = x+12 and m∠5 = 3x – 36. What is x? Given that k∥j, write a proof to show that ∠2 and ∠5 are supplementary.
3-4 The Triangle Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a triangle.
3-4 The Triangle Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a triangle.
3-4 The Triangle Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a triangle.
3-4 The Triangle Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a triangle.
3-4 The Polygon Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a polygon.
3-4 The Polygon Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a polygon.
3-4 The Polygon Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a polygon.
3-4 The Polygon Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a polygon.
3-4 The Polygon Angle Sum Theorem EQ: Determine the measures of interior and exterior angles of a polygon. homework: page 150 (1-6, 10-20) all page 161 (1-21) all