Polygons - Part 1 Triangles
Introduction Complementary Angles: are two angles that add up to 90 Example: degrees A ADB = 65 degrees Therefore B + ADB BDC 65 deg 25 deg D BDC = 25 degrees C 90 Degrees
Introduction Supplementary Angles: are two angles that add up to 180 degrees Example: Therefore, B ACB = 45 deg BCD = 135 deg + ACB BCD 45 deg 135 deg A C D 180 Degrees
Example The diagram below shows a transversal crossing two parallel lines. Record the angle measure on the diagram without measuring the angles. 160 a) What are the measures of two opposite angles in the diagram? b) What are the measures of two supplementary angles in the diagram?
Example The diagram below shows a transversal crossing two parallel lines. Record the angle measure on the diagram without measuring the angles. 160 20 160 a) What are the measures of two opposite angles in the diagram? 160 Degrees b) What are the measures of two supplementary angles in the diagram? 160 degrees and 20 degrees because the sum is 180 degrees
Properties of Triangles Triangle: a polygon with three straight sides and three vertices Vertex/Vertices: each angular point of a polygon Vertices } Side
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
Classification of Triangles Equilateral Triangle: A triangle where all three sides are the same length and all three angles are of equal measure Example:
Classification of Triangles Isosceles Triangle: A triangle where two sides are of equal length and two angles are of equal measure Example:
Classification of Triangles Scalene 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 180 degrees
Example 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. S a) What type of triangle is RST? 30 ft 30 ft b) What is the measure of RST? R 38 38 T How do you know?
Example 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. a) What type of triangle is RST? S Isosceles 30 ft 30 ft b) What is the measure of RST? 104 degrees R 38 38 T How do you know? 38 + 38 + 104 = 180 degrees
Quadrilaterals Which of the following shapes are polygons?
Quadrilaterals Which of the following shapes are polygons?
Definitions Polygon: a two dimensional, closed figure with straight sides intersecting at end points. Example: triangle, square, etc. Note: Circles are not polygons because they are round Quadrilateral: a polygon with four sides Example: rectangle
Types of Quadrilaterals Rectangle: a parallelogram that has four sides and four right angles
Types of Quadrilaterals 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 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
Regular Polygons A polygon that has all angles the same value and all sides the same value. Example: Are the following shapes regular polygons? a) b)