Download Smartboard 7.9 Notes.notebook

Smartboard 7.9 Notes.notebook
October 30, 2012
7.9 Exterior Angles
Jan 7­2:34 PM
Oct 30­9:46 AM
1
Smartboard 7.9 Notes.notebook
October 30, 2012
By looking at the exterior
of this house,
can you guess who calls this
place home?
Oct 29­6:45 AM
DEFINITION: An angle is an EXTERIOR ANGLE of a polygon if and only if it forms a linear pair with one of the angles of a polygon.
Jan 7­2:37 PM
2
Smartboard 7.9 Notes.notebook
October 30, 2012
77O
135O
148O
Jan 7­2:38 PM
77O
135O
148O
Insightful…is there anything you notice about the angles you just found, in relation to the given
triangle ABC?
77 = 32 + 45
135 = 103 + 32
148 = 103 + 45
Jan 7­2:38 PM
3
Smartboard 7.9 Notes.notebook
October 30, 2012
DEFINITION: Exterior Angle Theorem: In a triangle, the measure of an EXTERIOR angle is equal to the SUM OF THE TWO INTERIOR ANGLES at the 2 OPPOSITE vertices. Jan 7­2:44 PM
W + Y
W + X
X + Y
Jan 7­2:44 PM
4
Smartboard 7.9 Notes.notebook
October 30, 2012
DEFINITION: Exterior Angle Inequality :
In a triangle the measure of an EXTERIOR angle is greater than the measure of the INTERIOR ANGLE at each of the other 2 VERTICES .
Jan 7­2:49 PM
In this example at the right, find the measures of angles:
Jan 7­2:51 PM
5
Smartboard 7.9 Notes.notebook
October 30, 2012
DEFINITION: Unequal Sides Theorem: If two SIDES OF A TRIANGLE are not congruent, then the angles opposite them are NOT CONGRUENT and the LARGER angle is OPPOSITE the longer side.
Jan 7­2:55 PM
Arrange the angles, from smallest to largest. A
8
6
B
C
7
Jan 7­2:56 PM
6
Smartboard 7.9 Notes.notebook
October 30, 2012
DEFINITION: Unequal Angles Theorem: If two ANGLES OF A TRIANGLE are not congruent, then the sides OPPOSITE THEM are not congruent, and the LONGER side is OPPOSITE the larger angle.
Jan 7­2:53 PM
43o
QS
RS
Jan 7­3:04 PM
7
Smartboard 7.9 Notes.notebook
October 30, 2012
46o
84o
PQ
Jan 7­3:06 PM
8