Isosceles Triangle ABC
• Vertex Angle• Leg
• Base
• Base Angles
A
B C
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Theorem 4.6-Base Angles Theorem
• If two sides of a triangle are congruent,
• Then, the angles opposite them are congruent.
A
B C
Prove Theorem 4.6
• Given:
• Prove:
A
B C
_____ _____
AB AC
B C
Theorem 4.6-Base Angles Theorem
• The converse:• If two sides of a
triangle are congruent,
• Then, the angles opposite them are congruent.
A
B C
Theorem 4.7-Converse of the Base Angles Theorem
• If two angles of a triangle are congruent,
• Then the sides opposite them are congruent.
A
B C
Prove Theorem 4.7
• Given:
• Prove:
A
B C
_____ _____
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
• Then it is equilateral.
B
A C
Theorem 4.8-Hypotenuse-Leg (HL) Congruence Theorem
• If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of a second right triangle,
• Then the two triangles are congruent.
by the HL theorem.
FDE ABC
F
D ECB
A
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