Bellwork

1. Clickers Bellwork 115 • Find the measure of the missing angle • Find the coordinates of the midpoint of AB with endpoints A(-2,6) and B(10,4). • Find the distance between A and B 120 82 x

2. Section 8.2 Special Properties of Parallelograms

3. The Concept • Two days ago we began a discussion of the special properties of polygons • Today we’re going to look at a few special properties of parallelograms

4. Definition We’ve discussed parallelograms previously, but it would behoove us to formally define them • Parallelogram • Quadrilateral where both pairs of opposite sides are parallel Set of Parallel Sides Set of Parallel Sides

5. Theorems Theorem 8.3: If a quadrilateral is a parallelogram, then its opposite sides are congruent Theorem 8.4: If a quadrilateral is a parallelogram, then its opposite angles are congruent.

6. Example What is the values of x & y? Axis of symmetry Vertex

7. Example What is the values of x? Axis of symmetry Vertex

8. Example What is the value of x? Axis of symmetry Vertex

9. Theorems Theorem 8.5: If a quadrilateral is a parallelogram, then it’s consecutive angles are supplementary Theorem 8.6: If a quadrilateral is a parallelogram, then its diagonals bisect each other This makes sense, given our understanding of exterior angles

10. Example What is the value of x? Axis of symmetry Vertex

11. Example What is the value of x? Axis of symmetry Vertex

12. Example What is the value of x? Axis of symmetry Vertex

13. Homework • 8.2 • 1, 2, 3-11, 13-22, 30,31, 38,39

14. Example In EFGH, mG is 25o less than mH. Sketch EFGH. Find the measure of each interior angle. Then label each angle with its measure F F G G E E H H G F G F E H H E Axis of symmetry Vertex

15. Most Important Points • Opposite sides of a parallelogram are congruent • Opposite angles of a parallelogram are congruent • Consecutive angles of a parallelogram are congruent • Diagonals of a parallelogram are bisected