Transcript Exterior Angles of Triangle
Aim: What’s outside the triangle?
Do Now: Find the measure of angle z. B 36 0 A 47 0
z
C
Aim: Exterior Angles Course: Applied Geo.
Find the measure of angle z and x. B 47 + 36 = 83 36 0 The sum of the measure of the angles of a triangle 83 0 is 180 0.
A 47 0 97
z
0 C
x
0 D 47 + 36 +
z
= 180 83 +
z
= 180
z
= 97
ACB and
BCD are supplementary 97 +
x
= 180
x
= 83
Aim: Exterior Angles Course: Applied Geo.
remote interior angles E exterior angle B 144 0 0 36 0 47 + 97 = 144 A 47 0 97 0 C
ABC and
CDE are supplementary 36 +
z
= 180
z
= 144
Aim: Exterior Angles Course: Applied Geo.
remote interior angles exterior angle E B 36 0
z
0 A 47 0 36 + 97 = 133 97 0 C
CAB and
BAE are supplementary 47 +
z
= 180
z
= 133
Aim: Exterior Angles Course: Applied Geo.
B
x
A
y
C
w
An
exterior angle
of a triangle is an angle formed by a side of the triangle and the extension of another side of the triangle.
w
is an
exterior angle
of triangle ABC
x
&
y
are
nonadjacent interior
angles often called
remote interior
angles The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Exterior Angle Theorem
Aim: Exterior Angles
w = x + y
Course: Applied Geo.
Find the value of variable s 128.5
0 Exterior Angle Theorem s 0
s
0 + 13 0 = 128.5
0 13
s
0 = 115.5
0 0 Find the value of variable s s o o 50 o 50 o Isosceles triangle 130 o Base angles of an isosceles triangle are congruent.
Aim: Exterior Angles Course: Applied Geo.
Model Problems
In the diagram,
AB EF
, and m
x
70, and m
y
105, find m
z
.
A Q 105 =
y x
= 70 R B E S
z
35 70 T m
QTS = m
x = 70 alternate interior
s Exterior Angle Theorem 105 = 70 + z 35 = z
Aim: Exterior Angles Course: Applied Geo.
Model Problems
Explain
how you find m
3 if m
5 = 130 and m
4 = 70.
5 = 130 o 2 4 3 1 = 70 o m
5 is an exterior angle of a triangle.
Its measure equals the sum of m
3 + m
4, the remote interior angles of the triangle. Given that m
5 = 130 m
3 must be 60 0 , the difference between m
5 and m
4.
0 and m
4 = 70 0 ,
Aim: Exterior Angles Course: Applied Geo.
Model Problems In the diagram,
AC
BC
, and
BA
is
x
and
2
x
C 80 o 2x + 30 o D A
x
o o
x
o B Isosceles triangle m
DAC + m
CAB = 180 2x + 30 + x = 180 3x + 30 = 180 3x = 150 x = 50
Aim: Exterior Angles Course: Applied Geo.
Base angles of an isosceles triangle are congruent.
The measure of an exterior angle of a triangle is 120 0 . If the measure of one of the remote angles is 20 0 less than three times the other remote angle, find the measure of the two remote angles.
Exterior Angle Theorem 3x - 20 120 0 x = smaller of two remote angles 3x - 20 = larger of two 3x – 20 + x = 120 4x – 20 = 120 4x = 140 x = 35
x
= 35 = 85 120 0
Aim: Exterior Angles Course: Applied Geo.