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Triangles Today’s Objectives • To learn new strategies that will help find the measures of angles in a triangle • To review how to classify triangles Types of Triangles (by sides) • Equilateral • Isosceles • Scalene Equilateral Triangles • Definition: – A triangle with three congruent sides. • Example: Isosceles Triangles • Definition: – A triangle with two congruent sides. • Example: Scalene Triangles • Definition: – A triangle with no congruent sides. • Example: Types of Triangles (by angle) • Equiangular • Acute • Right • Obtuse Equiangular Triangles • Definition: – A triangle with three congruent angles. • Example: Acute Triangles • Definition: – A triangle whose angles are all acute. • Example: Right Triangles • Definition: – A triangle with one right angle. • Example: Obtuse Triangles • Definition: – A triangle with one obtuse angle. • Example: Triangle Video • Triangle video!! Triangle Activity 1. 2. 3. 4. Draw and cut out a large triangle. Number all three angles of the triangle Tear of the angles Place the 3 angles adjacent to each other to form one angle • • Compare your results with a partner. Draw conclusions about the sum of the angles of a triangle. Triangle Angle-Sum The sum of the measures of the angles of a triangle is always 180. Find the measure of the missing angle < C = 57° http://maths.fallibroome.cheshire.sch.uk/triangle.jpg http://www.mathsisfun.com/geometry/images/triangle-missing-angle.gif < a = 87° x < x = 45° x http://www.gizapyramid.com/basic_triangle_w-angles.gif Practice • Find all value for missing angels: <y +70+90=180 <y +160=180 <y=20 <x+40+90=180 <x+130=180 <x=50 Practice • Find all value for missing angels: <x +83+41=180 <x +123=180 <x=56 <x and <y are vertical angels and therefore, have the same measure Practice • Find all value for missing angels: <x + 39 + 65=180 <x +104=180 <x=76 <y + <x = 180 <y +76 = 180 <y = 104 <z + <y + 21 = 180 <z + 104 +21 = 180 <z + 125 = 180 <z = 55 Find the following angle measures. B 45° C 123° 57° <FDC <ADF <FDC <CDB <CDBangles are The following <D 74++106 90++angles D57 == 180 180 The<D following are + 123 + 45 = 180 supplementary = 180° <D 164++163 D == =180 180 supplementary 180° + 168angle = 180 74 + <D missing = 180° <D D angle ==16 17= 180° 57 + missing <Dangle = 12= 106 ° Missing Missing angle = 123° F 106° 74° A D Homework Triangles