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Transcript

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 (1800) 3 equal sides 2 equal sides Aim: Isosceles Triangle No equal sides Course: Applied Geometry Isosceles Triangle Isosceles Triangle A triangle with two sides that are equal in length. AB BC B leg A leg Base angles Base C Base angles of an isosceles triangle are congruent Course: Applied Geometry Aim: Isosceles Triangle 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: mABQ = mCBQ Angle bisector of a triangle - A line segment that divides an angle a triangle into Course: twoApplied halves. Aim: of Isosceles Triangle 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. F E H Angle bisector - A line segment that divides an angle of a triangle into two halves. G Median - A line segment from a vertex to the midpoint of the opposite side. 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 Model Problem I Complete each statement. Explain. a. KI _____ b. KN ____ N c . ML _____ K L M J Aim: Isosceles Triangle Course: Applied Geometry Model Problem Find the measure of the vertex angle of an isosceles triangle if a base angle measures: A. 44o 180o - (44o + 44o) 180o - (88o) = 92o 92o 44o 44o Find the measure of the base angles of an isosceles triangle if the vertex angle measures: B. 44o 44o 180o - 44o = 136o 2x = 136o x = 68o o o x68 Aim: Isosceles Triangle 68xoo Course: Applied Geometry Model Problem B Triangle ABC is isosceles with AB BC, AB = 3x - 2 and BC = 5x – 14. Find the value of x: 16 16 C A 3x - 2 = 5x - 14 -3x -3x - 2 = 2x - 14 +14 +14 +12 = 2x 6=x Aim: Isosceles Triangle 3x - 2 3(6) - 2= 16 5x - 14 5(6) - 14= 16 Course: Applied Geometry Model Problem The measure of the vertex angle of an isosceles triangle is 100o. 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 1800. 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. B What the diagram tells me: BC AB ABC is isosceles x A CBD ABD ( x) y 90 angle bisector 63 mCDB = 90 = m y D C In an isosceles triangle, the angle bisector and altitude drawn from the vertex angle, are the same line. 63 + 90 + CBD = 180 mCBD = 54 = mx C A = 63 Aim: Isosceles Triangle Sum of angles of a triangle equal 180. Base angles of an isosceles triangle are congruent Course: Applied Geometry Equilateral Triangle An equilateral triangle has three equal sides. R P O If a triangle is equilateral, then it is equiangular with each angle of the triangle measuring 60o. 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. x 65 x Find x. Aim: Isosceles Triangle Course: Applied Geometry Model Problem Find x. Find m & n. W 50 Z m x V n Y VQ and YZ are angle bisectors Aim: Isosceles Triangle Course: Applied Geometry Model Problem In triangle ABC, mA = x – 2, mB = 3x + 20 and mC = 5x. Find the value of x and the measure of each angle mA + mB + mC = 180. x – 2 + 3x + 20 + 5x = 180 9x + 18 = 180 - 18 - 18 9x = 162 mA = x - 2 9 9 18 - 2 = 16 x = 18 mB = 3x + 20 3(18) + 20 = 74 mC = 5x 5(18)= 90 Aim: Isosceles Triangle What type of triangle is this? Right Triangle Course: Applied Geometry