4.6 the isosceles triangle theorems base angles and opposite sides hypotenuse - leg
TRANSCRIPT
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4.6 The Isosceles 4.6 The Isosceles Triangle Triangle
TheoremsTheoremsBase Angles and Opposite Base Angles and Opposite
SidesSides
Hypotenuse - LegHypotenuse - Leg
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Parts of an Isosceles Triangle
Vertex
legleg
base
anglebaseanglebase
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Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
A
B C
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Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.
Given:
Bisect angle A
So by SAS
So
By C.P.C.T.
A
B CD
ACAB
CADBAD
CADBAD
CB
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Corollary of Isosceles Triangle Theorem
An equilateral triangle is also equiangular
An equilateral triangle has three 60 degree angles.
The bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.
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Another Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
What is this compared to
the Isosceles Triangle Theorem?
An equiangular triangle is also equilateral.
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Solve for x and y
50
xy
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Solve for angles… 2,3,4
Given:
AB
C2
3 4
140
ACBC
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Hypotenuse – Leg (HL)
In two right triangles if the hypotenuse and one leg are congruent, then the triangles are congruent.
To use this you must show Right Triangles
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Solve for v
22 v
42 v
5v
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Find the missing side
62
6256
4142
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HomeworkHomework
Page 239 – 242 Page 239 – 242
##9 – 25 odd, 9 – 25 odd,
34 -37, 3934 -37, 39
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HomeworkHomework
Page 239 – 242 Page 239 – 242
##8 -24 even8 -24 even
29- 3329- 33