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GeometryLesson 4 – 2
Angles of Triangles
Objective:Apply the triangle Angle-Sum Theorem.
Apply the Exterior Angle Theorem.
Triangle Angle-Sum Theorem
Triangle Angle-Sum TheoremThe sum of the measures of the angles of a
triangle is 180.
Auxiliary line
Auxiliary line – an extra line or segment drawn in a figure to help analyze geometric relationships.
ABCGiven :
180321
:Pr
mmm
ove
Find the measure of each numbered angle.
Which angle do we find first?
Could find angle 2 first since we Know 2 other angles in that triangle. Or we could find angle 1 since we Know it forms a linear pair with 57.
18071572 m1801282 m522 m
180571 m1231m
Since linear pair. Don’t get this 180 confused with adding all the angles of a triangle to 180.
1802813 mm180281233 m1801513 m293 m
Find the measure of each numbered angle.
18065587 m1801237 m577 m
18076 mm180576 m1236 m
575 m
1806754 mm18067574 m1801244 m564 m
180986 mmm18088123 mm57)8(2 m5.288 m5.289 m
Exterior & Remote interior angles
Exterior angles of a triangle:Formed by one side of the triangle and the
extension of an adjacent side. Exterior angle that is adjacent to the triangle.
Remote Interior anglesThe 2 interior angles inside the triangle that are not
adjacent to the exterior angle.
1 2
34
5
6
7
891011
12
Name an exterior angle and the pairof remote interior angles that go with it.
2&14 Exterior Remote Int.
2&16 3&17 3&19 3&210 3&212
Angles 5, 8, and 11 are not exterior angles since they are not adjacent to a side of the triangle.
Theorem
Exterior Angle TheoremThe measure of an exterior angle of a
triangle is equal to the sum of the measures of the two remote interior angles.
Find the measure of angle FLW.
2x – 48 = x + 32 Exterior angle = Sum of Remote Interior angles
x – 48 = 32x = 80
11248)80(2482 xFLW
Corollary
Corollary – A theorem with a proof that follows as a
direct result of another theorem.
Corollaries
Corollary 4.1The acute angles of a right triangle are
complementary.
Corollary 4.2There can be at most one right or obtuse
angle in a triangle.
Find the measures of each numbered angle.
18052901 m1801421 m381m18038902 m1801282 m522 m9023 mm90523 m383 m
1809034 mm18090384 m1801284 m524 m
90382 mor
Find the measures of each numbered angle.
90415 m495 m
90483 m423 m
56
104
1801052 m762 m
1041m
1805624 mm18056764 m1801324 m484 m
Homework
Pg. 248 1 – 11 all, 12 – 40 EOE, 50, 60, 64, 66