Technical GeometryChapter 6Sections 1 & 2 : Technical GeometryChapter 6Sections 1 & 2
Slide 2 : A POLYGON IS A PLANE Figure formed by 3 or more segments. A POLYGON IS A flat shape with 3 or more straight sides.
Slide 3 : Is this a polygon? YES YES NO
Slide 4 : Is this a polygon? YES no NO
Slide 5 : Is this a polygon? no yes yes
Slide 6 : Is this a polygon? yes no no
Slide 7 : A diagonal connects two non-adjacent vertices
Slide 8 : A diagonal connects two non-adjacent vertices
Slide 9 : What connects two adjacent vertices? sides
Slide 10 : Polygons are classified by the number of sides triangle 3 sides
3 angles 3 vertices
Slide 11 : Polygons are classified by the number of sides quadrilateral 4 sides
4 angles 4 vertices
Slide 12 : Polygons are classified by the number of sides pentagon 5 sides
5 angles 5 vertices
Slide 13 : Polygons are classified by the number of sides hexagon 6 sides
6 angles 6 vertices
Slide 14 : Polygons are classified by the number of sides heptagon 7 sides
7 angles 7 vertices
Slide 15 : Polygons are classified by the number of sides octagon 8 sides
8 angles 8 vertices
Slide 16 : Polygons are classified by the number of sides Nonagon 9 sides
9 angles 9 vertices
Slide 17 : Polygons are classified by the number of sides Decagon 10 sides
10 angles 10 vertices
Slide 18 : Polygons are classified by the number of sides doDecagon 12 sides
12 angles 12 vertices
Slide 19 : Polygons are classified by the number of sides 14 - gon 14 sides
14 vertices
Slide 20 : Polygons are classified by the number of sides n - gon ? sides
? vertices
Slide 21 : Polygons are classified by the number of sides 28 - gon 28 sides
28 vertices
Slide 22 : How can you draw a polygon with 9 sides? Start with 9 vertices Place them circularly Connect with segments
Slide 23 : draw a polygon with 11 sides Draw 11 vertices
Slide 24 : draw a polygon with 5 sides Draw 5 vertices
Slide 25 : Sum of the measures of the interior angles of a quadrilateral is 360 90o 90o 90o 90o 90o + 90o + 90o + 90o = 360o
Slide 26 : Sum of the measures of the interior angles of a quadrilateral is 360 120o xo 40o 40o + 140o + 120o + xo = 360o 140o 300o + xo = 360o xo = 60o
Slide 27 : Sum of the measures of the interior angles of a quadrilateral is 360 80o xo 80o 80o + 100o + 80o + xo = 360o 100o 260o + xo = 360o xo = 100o
Slide 28 : Sum of the measures of the interior angles of a quadrilateral is 360 90o xo 90o 90o + 90o + 95o + xo = 360o 95o 275o + xo = 360o xo = 85o
Slide 29 : Sum of the measures of the interior angles of a quadrilateral is 360 30o xo 170o 170o + 30o + 115o + xo = 360o 115o 315o + xo = 360o xo = 45o
Slide 30 : How can we remember . . . The Sum of the measures of the interior angles of a quadrilateral is 360 ? Draw a diagonal and get. . . . . . TWO Triangles Sum of the angles of a triangle is 180… x 2 = 360 180 180
Slide 31 : Introducing. . .
A very special quadrilateral! parallelogram parallelogram parallelogram
Slide 32 : parallelogram parallelogram parallelogram FIVE facts you must know about me I have two pairs of opposite sides that are parallel #1
Slide 33 : parallelogram parallelogram parallelogram I have two pairs of opposite sides that are congruent #2 15 15 8 8
Slide 34 : parallelogram parallelogram parallelogram I have two pairs of opposite angles that are congruent #3 110o 110o 70o 70o Congruent Congruent Congruent
Slide 35 : parallelogram parallelogram parallelogram My consecutive angles are supplementary (sum to 180) #4 100o 100o 80o 80o Supplements Supplements Supplements
Slide 36 : parallelogram parallelogram parallelogram My diagonals cut each other in half #5 My diagonals bisect each other 7 7 5 5
Slide 37 : parallelograms parallelograms parallelograms 1. Have both pairs of opposite sides parallel 2. Have both pairs of opposite sides congruent 3. Have both pairs of opposite angles congruent 4. Have consecutive angles which are supplementary 5. Have diagonals that bisect each other
Slide 38 : 7 The figure is a parallelogram ? 7 3.1 ? 3.1
Slide 39 : 80o The figure is a parallelogram ? 80o ? 100o ? 100o
Slide 40 : 14 The figure is a parallelogram ? 14 17 ? 17
Slide 41 : 5 The figure is a parallelogram ? 5 8 ? 8 12 ? 6 ? 6 8 ? 4 ? 4