5.5‐ An Inequality Involving an Exterior Angle of a Triangle
EXTERIOR ANGLE OF A POLYGON
‐an exterior angle of a polygon is an angle that forms a linear pair with one of the interior angles of the polygon
‐an exterior angle of a triangle is formed outside the triangle by extending a side of the triangle
‐for each exterior angle‐‐‐>there are 1 adjacent interior angles
and 2 nonadjacent interior angles
‐‐‐‐‐>Theorem: the measure of an exterior angle of a triangle is greater than the measure of either nonadjacent interior angle
1
Use triangle ABC, where D is a point on AB.
a) Name the exterior angle
of triangle DCB at vertex D.
b) Name the 2 nonadjacent
interior angles of triangle DCB
for the exterior angle given
as the answer to a
c) Write the theorem that allows
us to say: m ADC > m DCB
d) Write the postulate that allows us to say:
m ACB > m DCB
2
Given: Isosceles triangle PQR
PS bisects vertex RPQ RSQ is extended through Q and T
Prove: a) m PQT > m QPS
b)m PQT > m RPS
3
Given: In triangle RST, Q is a point on RT
P is a point on ST
QT≅PT
Prove: m SPQ > m QPT
4
Homework:
5.5 pg 193 #1‐13odd,18,19
5