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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
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