1. Javier Mendez

2. A polygon is any shape that is closed, has more than two sides and it does not have curved sides. In a polygon, the segments cannot intersect each other. Every polygon has sides vertices and they may have diagonals. diagonal side vertex Not a Polygon

3. When a polygon has a vertex pointing in, it is a concave polygon. The flag of Nepal is a concave polygon. When all of the vertices are pointing outside, it is a convex polygon. These figures are convex polygons. Convex

4. Equilateral: When all of the sides of a polygon are congruent. Equiangular: When all of the angles of a shape are congruent.

5. The sum of the interior angles of a convex polygon will always be the number of sides the polygon has, minus 2 times 180. Octagon8 – 2 = 6 6 x 180 = 1080 1080 degrees The sum of a 100-gon is:The sum of a 78-gon is: 100 – 2 = 98 x 180 = 17640 degrees78 – 2 = 76 x 180 = 13680 degrees

6. A parallelogram is a shape that has two pairs of parallel sides in it. Properties of Parallelograms: 1)In a parallelogram, opposite sides are congruent. 2)In a parallelogram, opposite angles are congruent. 3)In a parallelogram, consecutive angles are supplementary. 4)In a parallelogram, diagonals bisect each other. A B C D B = D A = C

7. A B C D E AE = ED CE = EB A B C D A AND D ARE SUPP. C AND B ARE SUPP.

8. A B C D A AND B ARE SUPP.

9. If a quadrilateral has one pair of congruent and parallel sides, it is a parallelogram. *The rest of the reasons where shown previpusly. Tell if the following quadrilaterals are parallelograms: A B C D E GIVEN: DE= 48 EB= 49 IT IS NOT A PARALLELOGRAM

10. A B C D GIVEN: DB ll AB YES IT IS A B C DGIVEN: AD ll BC IT IS NOT A PARALLELOGRAM BECAUSE WE DON’ T KNOW IF THEY ARE CONGRUENT. A BC D GIVEN: X = 10 ANGLE D = X * 9 + 5 ANGLE B = 85 + X ANGLE C AND A ARE CONGRUENT TO EACH OTHER. IT IS A PARALLELOGRAM

11. IT IS NOT A PARALLELOGRAM

12. A rectangle is a quadrilateral with 4 right angles A rectangle is a parallelogram Its diagonals are congruent A rhombus is a qudrilateral with 4 congruent sides It is a parallelogram Its diagonals are perpendicular Diagonals bisect a pair of opposite angles A square is a quadrilateral with all of the sides congruent and all of the angles too It is a rectangle, a rhombus and a parallelogram.

13. Tell if the following shapes are squares, rectangles or rhombus A B C D GIVEN: CA = DB RECTANGLE A B C D GIVEN: ANGLE A AND D ARE 45 IT IS A RHOMBUS GIVEN: ONE OF THE ANGLES = 90 IT IS A SQUARE

14. GIVEN: A, B, C, D ARE CONGRUENT IT IS A RHOMBUS A B C D GIVEN: ONE ANGLE IS 90 IT IS A RECTANGLE

15. A trapezoid is a quadrilateral that has a pair of parallel sides. In an isosceles trapezoid the pairs of base angles are congruent. When a trapezoid has a pair of congruent base angles, it is isosceles When a trapezoid is isosceles, it has congruent diagonals The midsegment of a trapezoid is parallel to both bases and its lenght is one half of the sum od the lenghts of the bases. Is it isosceles? Yes Is this an isosceles trapezoid? A C D AC > BD NO B

16. A B C D AD = 3.2 METERS BC = 2.9 METERS IS THIS TRAPEZOID ISOSCELES? NO

17. 28 WHAT IS THE SUM OF THE TWO BASES? 56 THE SUM OF THE BASES IS 100, WHAT IS THE LENGHT OF THE MIDESEGMENT? 50

18. A kite is quadrilateral with two pairs of consecutive congruent sides. Its diagonals are perpendicular One pair of opposite angles is congruent. IS THIS A KITE? YES IS THIS A KITE? NO 26 25.7

19. IS THIS A KITE? GIVEN: X = 8, Y = 4 YES X * 316 + X Y * 3Y + 8 45 IS THIS A KITE? YES