LESSON 3.2B – CLASSIFYING TRIANGLES Geometry Notes T.2.G.2 Investigate the measures of segments to determine the existence of triangles ( triangle inequality theorem ) CGT.5.G.3 Determine, given a set of points, the type of figure based on its properties ( parallelogram, isosceles triangle, trapezoid )

D EFINITIONS Polygon: A closed figure with three or more sides Triangle: A three-sided polygon whose angles add to 180 degrees Vertices: The points where two sides of a polygon intersect

Name the following based on this triangle: Triangle: Sides: Vertices: Angles: What is the side opposite angle A? What is the angle opposite side AC? A BC

C LASSIFYING T RIANGLES BY A NGLES NameDescriptionPicture

C LASSIFYING T RIANGLES BY S IDES NameDescriptionPicture

R IGHT T RIANGLE Hypotenuse – Leg – Side opposite Y: Angle opposite : Angle opposite the hypotenuse: Side opposite the right angle: Name the legs: X Y Z

I SOSCELES T RIANGLE Legs – Base Angles – Vertex Angle - A B C

E XAMPLES Classify the following triangles by their sides: A triangle with sides 5x, 5x, and 5x A triangle with sides 3, 6, and 7 A triangle with sides 6, 8, and 8

E XAMPLES Classify the following triangles by their angles: A triangle with angles 25°, 37°, and 118° A triangle with angles 60°, 60°, and 60° A triangle with angles 30°, 60°, and 90°

E XAMPLES Sketch the following triangles. If not possible, write not possible: An obtuse, scalene triangle A right, equilateral triangle An acute, isosceles triangle An equiangular, isosceles triangle

E XAMPLE Using the distance formula and the coordinates of triangle ABC, classify the triangle. 1. A(-4, 2) B(2,2) C(2, -3)

NOW YOU TRY… Using the distance formula and the coordinates of triangle ABC, classify the triangle. 2. A( -1, 0) B(0, 3) C(2, -3)