Aim: Isosceles Triangle Course: Applied Geometry Aim: What is an Isosceles Triangle? Do Now: What type of triangle has sides of 3, 6, 8?

Aim: Isosceles Triangle Course: Applied Geometry Triangles A triangle is a three sided polygon enclosing three angles. The sum of the measure of the angles of a triangle is 180 degrees (180 0 ) 3 equal 2 equal No equal sides sides sides

Aim: Isosceles Triangle Course: Applied Geometry Isosceles Triangle A triangle with two sides that are equal in length. AB  BC A C B leg Base angles Base Base angles of an isosceles triangle are congruent Isosceles Triangle leg

Aim: Isosceles Triangle Course: Applied Geometry The Special Lines of a Triangle Altitude BH is an altitude from B to AC Altitude of a Triangle - A line segment from a vertex and perpendicular to the opposite side. Angle Bisector BQ is the bisector of  B: m  ABQ = m  CBQ Angle bisector of a triangle - A line segment that divides an angle of a triangle into two halves.

Aim: Isosceles Triangle Course: Applied Geometry Median BM is the median from B to the midpoint of AC: AM = MC Median of a triangle - A line segment from a vertex of a triangle to the midpoint of the opposite side. Special lines of various triangles

Aim: Isosceles Triangle Course: Applied Geometry Special Lines of an Isosceles Triangle Altitude - line segment from a vertex and perpendicular to the opposite side. Median - A line segment from a vertex to the midpoint of the opposite side. Angle bisector - A line segment that divides an angle of a triangle into two halves. In an isosceles triangle, all of three of these lines, drawn from the vertex angle, are the same line.

Aim: Isosceles Triangle Course: Applied Geometry Complete each statement. Explain. Model Problem

Aim: Isosceles Triangle Course: Applied Geometry Find the measure of the vertex angle of an isosceles triangle if a base angle measures: A. 44 o 180 o - (44 o + 44 o ) 180 o - (88 o ) = 92 o 92 o 44 o Find the measure of the base angles of an isosceles triangle if the vertex angle measures: B. 44 o 180 o - 44 o = 136 o 2x = 136 o x = 68 o xoxo xoxo 68 o 44 o Model Problem

Aim: Isosceles Triangle Course: Applied Geometry Triangle ABC is isosceles with AB  BC, AB = 3x - 2 and BC = 5x – 14. Find the value of x: 3x - 2 = 5x x - 2 = 2x = 2x 6 = x 3(6) - 2= 16 3x - 2 5x (6) - 14= 16 Model Problem A B C 3x - 2 5x

Aim: Isosceles Triangle Course: Applied Geometry Model Problem The measure of the vertex angle of an isosceles triangle is 100 o. Find the number of degrees in one of the base angles of the triangle. If the degree measure of each angle of a triangle is 60, which of the following statements is false? a)The triangle is equiangular b)The triangle is equilateral c)The triangle is scalene. d)The sum of the measure of the interior angles of the triangle is Find the degree measure of each of the acute angles of an isosceles right triangle.

Aim: Isosceles Triangle Course: Applied Geometry Model Problem Find the values of x and y.  ABC is isosceles BC  AB  CBD   ABD  C   A = 63 What the diagram tells me: Base angles of an isosceles triangle are congruent m  CBD = 54 = m  x m  CDB = 90 = m  y In an isosceles triangle, the angle bisector and altitude drawn from the vertex angle, are the same line. angle bisector  CBD = 180 Sum of angles of a triangle equal 180. ( x)( x) 90

Aim: Isosceles Triangle Course: Applied Geometry Equilateral Triangle If a triangle is equilateral, then it is equiangular with each angle of the triangle measuring 60 o. An equilateral triangle has three equal sides. All three special lines drawn from the each angle of an equilateral triangle are the same line.

Aim: Isosceles Triangle Course: Applied Geometry Model Problem Find x.

Aim: Isosceles Triangle Course: Applied Geometry Model Problem Find x. VQ and YZ are angle bisectors Find m & n.

Aim: Isosceles Triangle Course: Applied Geometry In triangle ABC, m  A = x – 2, m  B = 3x + 20 and m  C = 5x. Find the value of x and the measure of each angle x – 2 + 3x x = 180 9x + 18 = x = x = 18 m  A = x - 2 m  B = 3x + 20 m  C = 5x = 16 3(18) + 20 = 74 5(18)= 90 What type of triangle is this? Right Triangle Model Problem m  A + m  B + m  C = 180.