1. Do Now: What is the distance between (1, -3) and (5, -4)?
If two parallel lines go through the following point…what is the missing y-value in Line B?
Lesson 3-4: Polygons

2. What is the distance between (1, -3) and (5, -4)?
Lesson 3-4: Polygons

3. If two parallel lines goes through the following point…what is the missing y-value in Line B?
We have to find the slope of Line A.
We have to find the equation of Line B using the given coordinate point.
We have to plug in 3 for x in our equation to find our y-value.
Lesson 3-4: Polygons

4. Lesson 3-4: Polygons

5. Lesson 3-4: Polygons

6. Geometry: Coordinate Geometry
Polygons

7. Polygons
Definition:
A closed figure formed by line segments so that each segment intersects exactly two others, but only at their endpoints.
These figures are not polygons
These figures are polygons

8. Polygon Names 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon
Hexagon
7 sides
Heptagon
8 sides
Octagon
9 sides
Nonagon
10 sides
Decagon
Dodecagon
12 sides
n sides
n-gon

9. Triangles and Quadrilaterals

10. Classifying Triangles by Sides
Scalene:
A triangle in which all 3 sides are different lengths. B C A A B C
Isosceles:
A triangle in which at least 2 sides are equal. G H I
Equilateral:
A triangle in which all 3 sides are equal.

11. Classifying Triangles by Angles
Acute:
A triangle in which all 3 angles are less than 90˚. 57 47 76 G H I
Obtuse:
108 44 28 B C A
A triangle in which one and only one angle is greater than 90˚& less than 180˚

12. Classifying Triangles by Angles
Right:
A triangle in which one and only one angle is 90˚
Equiangular:
A triangle in which all 3 angles are the same measure.

13. Classification by Sides with Flow Charts & Venn Diagrams
polygons
Polygon
triangles
Triangle
scalene
isosceles
Scalene
Isosceles
equilateral
Equilateral

14. Classification by Angles with Flow Charts & Venn Diagrams
polygons
Polygon
triangles
Triangle
right
acute
equiangular
Right
Obtuse
Acute
obtuse
Equiangular

15. What is a Quadrilateral?
All quadrilaterals have four sides.
They also have four angles.
The sum of the four angles totals 360°

16. Parallelogram Two sets of parallel sides Two sets of congruent sides.
The angles that are opposite each other are congruent.
The diagonals of a parallelogram bisect each other

17. Rectangle Has all properties of quadrilateral and parallelogram
A rectangle also has four right (90°) angles.
The two diagonals are congruent

18. Rhombus
A rhombus has all the properties of a quadrilateral and all the properties of a parallelogram, in addition to other properties.
All four sides are equal (A rhombus is sometimes referred to as a “slanted square”)
Diagonals of a rhombus create a 90° angle

19. Square
Squares have all the properties of a quadrilateral, all the properties of a parallelogram, all the properties of a rectangle, and all the properties of a rhombus.
A square has all sides equal

20. Trapezoid
These parallel sides are opposite one another. The other set of sides are non parallel.

21. Isosceles Trapezoid Non-parallel sides are equal
Both pair of base angles in an isosceles trapezoid are also congruent.

22. Right Trapezoid
A right trapezoid also has one set of parallel sides, and one set of non-parallel sides.
A right trapezoid has exactly two right angles. This means that two angles measure 90°.

23. Quadrilateral Family Tree
It’s important to have a good understanding of how each of the quadrilaterals relate to one another.
Any quadrilateral that has two sets of parallel sides can be considered a parallelogram.
A rectangle and rhombus are both types of parallelograms, and a square can be considered a rectangle, rhombus, and a parallelogram.
Any quadrilateral that has one set of parallel sides is a trapezoid. Isosceles and Right are two types of trapezoids.
Parallelogram
Trapezoid
Rectangle
Rhombus
Isosceles
Trapezoid
Right
Trapezoid
Square

24. Lesson 3-4: Polygons

25. Lesson 3-4: Polygons

26. Lesson 3-4: Polygons

27. Prove that quadrilateral A(1,2), B(2,5), C(5,7) and D(4,4) is a parallelogram by using slopes.
Lesson 3-4: Polygons

28. Prove that A(1,1), B(4,4), C(6,2) are the vertices of a right triangle.
Lesson 3-4: Polygons

29. Word Bank: Regular polygon Decagon Bases Rectangle Legs
Convex (4 down)
Concave(16 down)
Polygon
Isosceles trapezoid
Quadrilateral
Vertex
Kite
Dodecagon
Diagonal
Rhombus
Parallelogram
Square
Base angles
Lesson 3-4: Polygons