1. By: Gabriel Morales Journal Chapter 6

2. 3 I want Corrected (0-10 pts.) 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. _____(0-10 pts.) Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples. _____(0-10 pts.) Describe the 4 theorems of parallelograms and their converse and explain how they are used. Give at least 3 examples of each. _____(0-10 pts.) Describe how to prove that a quadrilateral is a parallelogram. Include an explanation about theorem 6.10. Give at least 3 examples of each. _____(0-10 pts.) 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. _____(0-10 pts.) Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each. _____(0-10 pts.) Describe a kite. Explain the kite theorems. Give at least 3 examples of each. _____(0-10 pts.) Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of each. _____(0-10 pts.) Describe the 3 area postulates and how they are used. Give at least 3 examples of each.

3. _____(0-10 pts.) Describe how to prove that a quadrilateral is a parallelogram. Include an explanation about theorem 6.10. Give at least 3 examples of each. To do this we must know the definition of Quadrilateral is a 4 sided figure. A parallelogram has many properties to it Def.: 4 sided figure with 2 sets of parallel lines 1. All 4 opposite sides are congruent 2. Opposite angles are congruent 3. One pair of sides are parallel and congruent 4. Diagonals Bisect 5. Adjacent/ Consecutive angles are supplementary 6. Theorem 6.10 states that if a quadrilateral is a parallelogram then its opposite sides are congruent.

4. _____(0-10 pts.) 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. Square: All Sides are Right Angles Equilateral and Equiangular Diagonals Bisect Diagonals are Perpendicular Adjacent/Consecutive Angles are supplementary Rectangles: A parallelogram with 4 right angles All < are right angles Diagonals are Congruent Rhombus: All sides are congruent Diagonals are Perpendicular

5. _____(0-10 pts.) Describe a trapezoid. Explain the trapezoidal theorems. Give at least 3 examples of each.. Trapezoid: 1.Both pairs of base angles are congruent 2.A quadrilateral with one pair of parallel lines 3.Diagonals are Congruent Iscoceles- Legs or 2 non parallel sides are congruent Midsegment Formula b1+b2 /2

6. _____(0-10 pts.) Describe a kite. Explain the kite theorems. Give at least 3 examples of each. Kite: One pair of congruent opposite sides. Longer Diagonal bisects the shorter diagonal (Perpendicular) One Pair of congruent opposite angles. 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.

7. _____(0-10 pts.) Describe how to find the areas of a square, rectangle, triangle, parallelogram, trapezoid, kite and rhombus. Give at least 3 examples of each. Rectangle/ Square B X H Ex B 5 H5 Area = 25 B7 H7 Area = 49 H4 B 5 Area - 20 Triangle: B X H /2 A = (5 x 6)/2= 15 A= 7 x 5 /2 = 17.5 A = 8 x 8 / 2 = 32 Parallelograms B X H Ex 5x 3 = 15 5 x 6 = 30 5 x 10 = 50 Trapezoid: A= a (b1 + b2) /2 a is the altitude Area of top triangle plus bottom triangle Rhombus B X H Ex B 5 H5 Area = 25 B7 H7 Area = 49 H4 B 54Area = 16

8. _____(0-10 pts.) 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. Polygons: polygons are closed figures made of 3 or more straight lines. Polygons include sides, vertices, and diagonals Sides: the sides are the points that meet at vertices. Vertices: They are where the sides of the polygon meet Diagonals: They are the imaginary lines that go from one of the vertices to the opposite angles.

9. Concave Concave polygons are those who have an interior angle that is more than 180 degrees. Or a side that goes inside the polygon. (angles push in)

10. Convex Convex is when no interior angles push in.

11. Equiangular All angles are the same! Like in a square or rectangle!

12. Equilateral All sides are congruent! Like in a rhombus, a square!

13. _____(0-10 pts.) Explain the Interior angles theorem for quadrilaterals. Give at least 3 examples. How many sides are there?Then subtract 2 from the # of sides…Then multiply by 180 to find the degrees of the quadrilateral! Ex Rhombus has 4 sides so go 4-2 times 180 which equals 360!! Ex 3-2 x 180 = 180! 5 – 2 x 180 = 540

14. 4 theorems of Parallelograms When one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram Converse: it is a parallelogram if if a pair of opposite sides are congruent and parallel.

15. 2nd When both pairs of opposite sides of quadrilaterals are congruent the quadrilateral is a parallelogram Converse: It is a parallelogram if both of the opposite sides are congruent.

16. 3rd When an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram Converse: It is a parallelogram if the angle is supplementary to both of its consecutive angles.

17. 4th When the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram Converse: It is a parallelogram if the diagonals bisect each other