1. Journal 6 By: Maria Jose Diaz-Duran

2. Describe what a polygon is. Include a discussion about the parts of a polygon. Also compare and contrast a convex with a concave polygon. Compare and contrast equilateral and equiangular. Give 3 examples of each. A polygon is closed figure formed by 3 or more segments. ConvexConcave No points to the center of the figure, no diagonal to the exterior also a regular polygon is always convex. If it goes to the center of the figure, contains points in the exterior of a polygon EquilateralEquiangular All sides are congruentA polygon in which all angels are congruent

3. Examples

4. Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples. The sum of the interior angle measures of a convex polygon with n sides is (n-2)180

5. Examples A. Find the sum of the interior angel measures of a convex octagon: (n-2)180 (8-2)180 1080 B. Find the measures of each interior angle of a regular nonagon Step 1: (n-2)180 (9-2)180 1260 Step 2: Find the measures of 1 interior angle 1260/9= 140 C. Find the measure of each interior angle of quadrilateral PQRS. (4-2)180=360 M<p + M<Q + M<R +M<S=360 C+ 3C+ C+ 3C=360 8C=360 C=45

6. Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each. TheoremsConverse If a quadrilateral is a parallelogram, then its opposite sides are congruent If its opposite sides are congruent, then a quadrilateral is a parallelogram If a quadrilateral is a parallelogram, then its opposite angles are congruent If the opposite angles are congruent, then a quadrilateral is a parallelogram If a quadrilateral is a parallelogram, then its consecutive angles are supplementary If its consecutive angles are supplementary then a quadrilateral is a parallelogram If a quadrilateral is a parallelogram, then its diagonal bisect each other If its diagonals bisect each other then a quadrilateral is a parallelogram

7. Examples If a quadrilateral is a parallelogram, then its opposite sides are congruent If a quadrilateral is a parallelogram, then its opposite angles are congruent If a quadrilateral is a parallelogram, then its consecutive angles are supplementary If a quadrilateral is a parallelogram, then its diagonal bisect each other

8. Describe how to prove that a quadrilateral is a parallelogram. Include an explanation about theorem 6.10. Give at least 3 examples of each. Theorems If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram If both pair of opposite angels of a quadrilateral are congruent then then quadrilateral is a parallelogram.

9. Examples If one pair of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram If both pair of opposite angels of a quadrilateral are congruent then then quadrilateral is a parallelogram.

10. Compare and contrast a rhombus with a square with a rectangle. Describe the rhombus, square and rectangle theorems. Give at least 3 examples of each. RectangleSquareRhombus A quadrilateral with four right angles. A quadrilateral with four right angles and four congruent sides A quadrilateral with four congruent sides. Theorems If a quadrilateral is a rectangle, then it is a parallelogram A quadrilateral is a square if and only if it is a rhombus and a rectangle. If a quadrilateral is a rhombus then its is a parallelogram If a parallelogram is a rectangle then its diagonals are congruent If a parallelogram is a rhombus then its diagonals are perpendicular If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles.

11. Examples

12. Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples each Trapezoid A quadrilateral with exactly one pair of parallel sides, each of the parallel sides is called a base and the nonparallel sides are called legs. Theorems Isosceles Trapezoids: if a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. if a trapezoid has one pair of congruent base angles, then the trapezoid is isosceles. A trapezoid is isosceles if and only if its diagonals are congruent Trapezoid Midsegment Theorems: The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

13. Examples

14. Describe a kite. Explain the kite theorems. Give at least 3 examples of each. Kite A quadrilateral with exactly two pairs of consecutive sides. Theorems If a quadrilateral is a kite, then its diagonals are perpendicular. If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

15. Examples If a quadrilateral is a kite, then its diagonals are perpendicular. If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

16. Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of each. Areas: SquareTo find the area of a square, multiply the lengths of two sides together (XxX=X2) RectangleTo find the area of a rectangle, just multiply the length times the width: (LxW) Triangle1/2 xbxh or bxh/2 ParallelogramTo find the area of a parallelogram, just multiply the base length (b) times the height (h) (BxH) Trapezoid½ H(B+b) KiteTo find the area of a kite, multiply the lengths of the two diagonals and divide by 2 (1/2AB) RhombusTo find the area of a rhombus, multiply the lengths of the two diagonals and divide by 2 (1/2AB)

17. Examples

18. Describe the 3 area postulates and how they are used. Give at least 3 examples of each. 1.Area of a Square Postulate: The area of a square is the square of the length of a side. 2.Area Congruence Postulate: If two closed figures are congruent then they have the same area. 3. Area Addition Postulate: The area of a region is the sum of the areas of its non- overlapping parts.

19. Examples Area of a Square Postulate Area Congruence Postulate Area Addition Postulate