Isosceles, Equilateral, and Right Triangles Sec 4.6

1
Isosceles, Equilateral, and Right TrianglesSec
4.6

• GOAL
• To use properties of isosceles, equilateral and
  right triangles
• To use RHL Congruence Theorem

2
Definitions

• Isosceles Triangle a triangle that has at least
  two congruent sides called legs.
• If a triangle has three congruent sides, it is
  called an Equilateral Triangle.

Vertex Angle
Leg
Leg
Base Angles
Base (noncongruent side)
Each angle measures 60 degrees
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Base Angles Theorem

• Base Angles Theorem If two sides of a triangle
  are congruent, then the angles opposite them are
  congruent.

A
C
B
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Converse of the Base Angles Theorem

• Converse of the Base Angles Theorem If two
  angles of a triangle are congruent, then the
  sides opposite them are congruent.

A
C
B
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Corollaries

• If a triangle is equilateral, then it is
  equiangular.
• If a triangle is equiangular, then it is
  equilateral.
• Is an equilateral triangle an isosceles triangle?
• Is an isosceles triangle an equilateral triangle?
  

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Example

• Find x and y.

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Hypotenuse Leg (HL) Congruence

• Hypotenuse Leg (HL) Congruence If the
  hypotenuse and a leg of a right triangle are
  congruent to the hypotenuse and a leg of a second
  right triangle , then the two triangles are
  congruent.

A
D
C
B
F
E
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Two Column Proof

• Given
• Prove

D
A
C
B
F
E
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Examples

• Find x or y

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Examples

• Are you given enough information to prove the
  triangles congruent?