Ch. 6 – Polygons and Quadrilaterals

1. Ch. 6 – Polygons and Quadrilaterals Jose Pablo Reyes

2. Describe what a polygon is. parts of a polygon. • Polygon: Any plane figure with 3 o more sides • Parts of a polygon: side – one of the segments that is part of the polygon Diagonal – a line that connects two vertices that are not a side Vertex – the point where two segments meet Interior angle – the angle that is formed inside the polygon by two adjacent sides Exterior angle – the angle that is formed outside the polygon by two adjacent sides

3. Polygon Examples

4. Describe convenx and concave polygons , equilateral and equiangular. • Convex polygon – is a polygon in which all vertices point out • Concave polygon – is a polygon in which at least one angle is pointing into the center of the figure • Equiangular – polygon in which all angles are congruent • Equilateral – polygon in which all sides are congruent

5. Convex and Concave, Equilangular and Equilateral polygons – Examples

6. Interior anglestheorem for quadrilaterals • Interior angles theorem of quadrilaterals:

7. Interior angle theorem of a quadrilateral Examples

8. 4 theorems of parallelograms and their converse • Theorem 6-2-4 : If a quadrilateral is a parallelogram its diagonals bisect each other converse: if the diagonals of a quadrilateral bisect each other then it is a parallelogram • Theorem 6-3-2: If both pairs of opposite sides of a quadrilateral are congruent, then it is a parallelogram converse: if in a quadrilateral both pairs of opposite sides are congruent then it is a parallelogram

9. Theorem 6-6-2: If a quadrilateral is a kite, then its diagonals are perpendicularconverse: if in a quadrilateral the diagonals are perpendicular, then it is a kite • Theorem 6-5-2: If the diagonals of a parallelogram are congruent, then it is a rectangleconverse: if a rectangle has congruent diagonals, then it is a parallelogram

11. How to prove a quadrilateral is a parallelogram – Theorem 6.10 • A quadrilateral is a parallelogram if; - opposite sides are parallel - opposite angles are congruent - opposite sides are congruent - adjacent angles are supplementary - diagonals bisect each other • Theorem 6.10:

12. Proving a quadrilateral is a parallelogram Examples

13. Comparing – Rhombuses, Squares and rectangles

14. Comparing: Rhombuses, Squares and rectangles – Examples

15. Rhombus Theorems • Theorem 6-4-3: If a quadrilateral is a rhombus, then it is a parallelogram • Theorem 6-4-4: If a parallelogram is a rhombus, then its diagonals are perpendicular • Theorem 6-4-5: If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

16. Rhombus Theorems – Examples

17. Rectangle Theorems • Theorem 6-4-1: If a quadrilateral is a rectangle, then it is a parallelogram • Theorem 6-4-2: If a parallelogram is a rectangle, then its diagonals are congruent

18. Rectangle Theorems – Examples

19. Trapezoid and its theorems • Trapezoid: A quadrilateral with one pair of parallel lines, each parallel side is called a base, and the parts that are not parallel are called legs. • Isosceles trapezoid: when the legs are congruent • Theorem 6-6-3: if a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent • Theorem 6-6-4: if a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles • Theorem 6-6-5: a trapezoid is isosceles if and only if its diagonals are congruent

20. Trapezoid Theorems – Examples

21. Trapezoid mid segment theorem • Theorem 6-6-6: The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases

22. Kite and its Theorems • Kite: A quadrilateral with two pairs of congruent consecutive sides • Theorem 6-6-1: if a quadrilateral is a kite, then its diagonals are perpendicular • Theorem 6-6-2: if a quadrilateral is a kite, then a pair of opposite angles are congruent

23. Kite – Examples

24. To find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus

25. 3 area postulates and how they are used