Polygons - Part 1Triangles and Quadrilaterals

Classification of Angles

Recall:

An angle that is exactly 90 degrees is a right angle

An angle that is greater than 0 degrees but less than 90 degrees is an acute angle

An angle that is more than 90 degrees but less than 180 degrees is an obtuse angle

IntroductionComplementary Angles: are two angles that add up to 90

degrees Example:

C

A

B

D

BDC = 25 degrees

ADB = 65 degrees Therefore

ADBBDC+

90 Degrees

65 deg25 deg

IntroductionSupplementary Angles: are two angles that add up to 180 degrees

Example:

CD

B

A

ACB = 45 deg BCD = 135 deg

Therefore,

ACBBCD+

180 Degrees

45 deg135 deg

Example

160°

a) What is the measure of the purple angle in the diagram?

b) What are the measures of the supplementary angles in the diagram?

The diagram below shows a transversal crossing two parallel lines. Record the angle measure on the diagram without measuring the angles.

Properties of Triangles

VerticesSide

}

Triangle: a polygon with three straight sides and three vertices

Vertex/Vertices: each angular point of a polygon

Classification of TrianglesEquilateral Triangle: A triangle where all three sides are the same length and all three angles are of equal measure

Example:

Classification of TrianglesIsosceles Triangle: A triangle where two sides are of equal length and two angles are of equal measure

Example:

Classification of TrianglesScalene Triangle: A triangle where no sides are of equal length and no angles are of equal measure.

Example:

Important Information

The sum of the interior angles of a triangle is always

equal to 180 degrees

Dawn plans to install a ridge vent on a roof. This will cool the attic. The angle of the vent needs to equal RST at the peak of the roof. Dawn knows the measurements in the diagram.

Example

a) What type of triangle is RST?

b) What is the measure of RST?

How do you know?

R

S

T

30 ft

38

QuadrilateralsWhich of the following shapes are polygons?

DefinitionsPolygon: a two dimensional, closed figure with straight sides intersecting at end points.

Example: triangle, square, etc.

Quadrilateral: a polygon with four sidesExample: rectangle

Note: Circles are not polygons because they are round

Types of Quadrilaterals

Rectangle: a parallelogram that has four sides and four right angles

Square: a rectangle having all four sides of equal length

Types of Quadrilaterals

Parallelogram: a four-sided figure with two pairs of parallel lines.

Types of Quadrilaterals

Rhombus: a parallelogram with opposite equal acute angles, opposite equal obtuse angles, and four equal sides

Types of Quadrilaterals

Trapezoid: a quadrilateral with only one pair of parallel sides

Types of Quadrilaterals

Kite: a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other rather than opposite one another.

Types of Quadrilaterals

A polygon that has all angles the same value and all sides the same value.

Example: Are the following shapes regular polygons? Why or why not?

a) b)

Regular Polygons

Irregular Quadrilateral:

A quadrilateral is a polygon with four sides. A regular polygon is a polygon with all sides and all angles congruent. An irregular quadrilateral is thus a quadrilateral that is not regular.

Example: Rectangle

Types of Quadrilaterals