Download Ch 5.4: Side Lengths of a Triangle Theorem: The sum of the lengths

Ch 5.4: Side Lengths of a Triangle
Theorem: The sum of the lengths of 2 sides of a triangle is greater than the length of the 3rd side
‐‐‐> we only need to add the 2 shorter sides to see whether their sum is greater than the 3rd
‐‐‐> Which of the following may be the lengths of the sides of a triangle?
(1) 2,3,5
(2) 4,4,8
(3) 3,4,8
(4) 5,6,7
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Two sides of a triangle have lengths 2 and 5. Find all possible lengths of the 3rd side.
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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
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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
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Given: In triangle ABC, D is a point on AC
AD≅BD
Prove: m ABC > m A
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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
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Homework:
5.4 pg 188 #1‐23odd
and
5.5 pg 193 #1‐13odd,16,18,19
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