Answer Key
University
High SchoolCourse
MPM1D | Principles of MathematicsPages
5
Academic year
2023
anon
Views
9
Angle Relationships in Triangles Goal: To learn angle properties. Vertex point where two or more lines meet. Interior angle angle formed on the inside of a polygon by two sides meeting at a vertex. Exterior angle angle formed on the outside of a geometric shape by extendi ng one of the lines past the vertex. The sum of the interior angles of a triangle is 180 β¦ β π΄π΅πΆ + β π΅πΆπ΄ + β πΆπ΄π΅ = 180 β¦ G.Sketchpad π β π΄π΅πΆ = 70. 70 β¦ π β π΅πΆπ΄ = 70. 70 β¦ π β πΆπ΄π΅ = 70. 70 β¦ π β π΄π΅πΆ + π β π΅πΆπ΄ + π β πΆπ΄π΅ = 180. 00 The sum of the exterior angles of a triangle is 360 β¦ Note that in angle names with three letters, the middle letter is always the vertex of the angle. Angle Properties Complementary Angles
Supplementary Angles Vertically Opposite Angles Exterior Angle of a Triangle Transversal Parallel Lines
Alternate Angles are Equal Corresponding Angles are Equal
Co-interior Angles Example: a) Find the measure of the exterior angle at vertex X . Explain your reasoning. I: π + 120 β¦ + 140 β¦ = 360 β¦ π + 260 β¦ = 360 β¦ π = 360 β 260 π = 100 Another way, II: π + 120 β¦ = 180 β¦ π = 180 β¦ β 120 β¦ π = 60 β¦ π + 140 β¦ = 180 β¦ π = 180 β¦ β 140 β¦ π = 40 β¦
So, the exterior angle at vertex X is π + π = 40 β¦ + 60 β¦ = 100 β¦ b) Helena says this exterior angle measures . 110 β¦ Is she right? Explain She is right since 40 β¦ + 70 β¦ = 110 β¦ (sum of the opposite interior angles is 110 π Another way: 40 β¦ + 70 β¦ + π¦ = 180 β¦ π¦ = 180 β 110 π¦ = 70 Since x and y are supplementary angles then π₯ + π¦ = 180 β¦ π₯ + 70 β¦ = 180 β¦ π₯ = 180 β 70 π₯ = 110
Angle Relationships in Triangles
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