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Isosceles Triangle ABC
• Vertex Angle
• Leg
A
• Base
• Base Angles
B
C
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Theorem 4.6-Base Angles
Theorem
• If two sides of a
triangle are congruent,
A
• Then, the angles
opposite them are
congruent.
B
C
Prove Theorem 4.6
_____
_____
• Given:
AB  AC
• Prove:
B  C
A
B
C
Theorem 4.6-Base Angles
Theorem
• The converse:
• If two sides of a
triangle are congruent,
A
• Then, the angles
opposite them are
congruent.
B
C
Theorem 4.7-Converse of the
Base Angles Theorem
• If two angles of a
triangle are congruent,
A
• Then the sides
opposite them are
congruent.
B
C
Prove Theorem 4.7
• Given:
B  C
_____
• Prove:
A
_____
AB  AC
B
C
Now that you know about these
theorems….test yourself with
some problems…
Solve for x and y
Solve for x and y
Solve for x and y
Corollary to theorem 4.6 & 4,7
• If a triangle is equilateral,
• Then it is equiangular
• If a triangle is equiangular
A
• Then it is equilateral.
B
C
Theorem 4.8-Hypotenuse-Leg
(HL) Congruence Theorem
A
• If the hypotenuse and
leg of a right triangle
are congruent to the
hypotenuse and leg of
a second right triangle,
F
B
D
• Then the two triangles
are congruent.
C
E
FDE 
ABC
by the HL  theorem.
Solve for x
Solve for x
Solve for x
Write the equation of the line
• Passing through P(1,1) and
• Perpendicular to y = -3x - 4
Given the points (5,8) & (-12,1)
• What is the distance between them?
• What are the coordinates of the midpoint?
Assignment 4.6