4.1 Triangles and Angles. Geometry Mrs. Spitz Fall 2004. Standard/Objectives:. Standard 3: Students will learn and apply geometric concepts. Objectives: Classify triangles by their sides and angles. Find angle measures in triangles
Standard 3: Students will learn and apply geometric concepts.
DEFINITION: A triangle is a figure formed by three segments joining three non-collinear points.
Triangles can be classified by the sides or by the angle
Equilateral—3 congruent sides
Isosceles Triangle—2 congruent sides
Scalene—no congruent sides
3 acute angles
Two sides sharing a common vertext are adjacent sides.
The third is the side opposite an angleParts of a triangle
Side opposite A
In the diagram you are given that C is a right angle. By definition, then ∆ABC is a right triangle. Because AC = 5 ft and BC = 5 ft; AC BC. By definition, ∆ABC is also an isosceles triangle.Identifying the parts of an isosceles triangle
About 7 ft.
Sides AC and BC are adjacent to the right angle, so they are the legs. Side AB is opposite the right angle, so it is t he hypotenuse. Because AC BC, side AB is also the base.Identifying the parts of an isosceles triangle
Hypotenuse & Base
About 7 ft.
Smiley faces are interior angles and hearts represent the exterior angles
Each vertex has a pair of congruent exterior angles; however it is common to show only one exterior angle at each vertex.
Exterior Angle theorem: m1 = m A +m 1
x + 65 = (2x + 10)
65 = x +10
55 = x