Proving Quadrilaterals: Theorems and Examples

Discover how various theorems and examples can help prove a quadrilateral is a parallelogram. Explore concepts like diagonal bisecting, congruent sides, and parallel angles. Learn the different ways to demonstrate the properties of quadrilaterals for a deeper understanding of geometry.

• Geometry
• Quadrilaterals
• Parallelogram
• Theorems
• Examples

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Uploaded on Apr 21, 2025 | 0 Views

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Presentation Transcript

1. 6 6- -3 Proving a Quadrilateral is 3 Proving a Quadrilateral is a Parallelogram a Parallelogram Geometry

2. Theorem 6-5: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

3. Example 1:

4. Theorem 6-6: If one pair of opposite sides is both congruent and parallel, then the quadrilateral is a parallelogram.

5. Example 2:

6. Theorem 6-7: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Ex. 3) Find x and y so that ABCD is a parallelogram.

7. Theorem 6-8: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Ex. 4) Find x and y so that ABCD is a parallelogram.

8. 5 Ways to Prove that a Quadrilateral is a Parallelogram: 1. Both pairs of opposite sides are parallel (Definition) 2.Diagonals bisect each other (Thm. 6-5) 3.One pair of opposite sides are both congruent and parallel (Thm. 6-6) 4.Both pairs of opposite sides are congruent (Thm. 6-7) 5.Both pairs of opposite angles are congruent (Thm. 6-8)