Proving that a Quadrilateral Is a Parallelogram

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6.3 Proving that a Quadrilateral is a Parallelogram

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Presentation transcript:

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 Proving That a Quadrilateral is a Parallelogram Lesson 6-3 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 (For help, go to Lesson 1-6 and 3-6.) Use the figure at the right for Exercises 1–4. Find the coordinates of the midpoints of and . What is the relationship between and ? Find the slopes of and . How do they compare? Are and parallel? Explain. What type of figure is ABCD? AC BD BD AC AB DC 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 (For help, go to Lesson 1-6 and 3-6.) Use the figure at the right for Exercises 1–4. Find the coordinates of the midpoints of and . What is the relationship between and ? AC BD 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 (For help, go to Lesson 1-6 and 3-6.) Use the figure at the right for Exercises 1–4. 2. Find the slopes of and . How do they compare? AC BD 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 (For help, go to Lesson 1-6 and 3-6.) Use the figure at the right for Exercises 1–4. 3. Are and parallel? Explain. AB DC 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 (For help, go to Lesson 1-6 and 3-6.) Use the figure at the right for Exercises 1–4. 4. What type of figure is ABCD? 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 THEOREM 6-5 If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 Proof of Theorem 6-5 Given: AC and BD bisect each other at E. Prove: ABCD is a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 Find values of x and y for which ABCD must be a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 THEOREM 6-6 If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 Find values of a and c for which PQRS must be a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 THEOREM 6-7 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 Proof of Theorem 6-7 Given: WX  ZY and XY  WZ Prove: WXYZ is a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 THEOREM 6-8 If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 Determine whether the quadrilateral is a parallelogram. Explain. a. b. 6-3

Proving that a Quadrilateral Is a Parallelogram GEOMETRY LESSON 6-3 The captain of a fishing boat plots a course toward a school of bluefish. One side of a parallel rule connects the boat with the school of bluefish. The other side makes a 36° angle north of due east on the chart’s compass. Explain how the captain knows in which direction to sail to reach the bluefish. 6-3