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Transcript 
Isosceles, Equilateral and
Right Triangle
Ch 4
Lesson 6
Name of Angles in a Triangle
Vertex Angle
Base
Base Angles
In an Isosceles Triangle…..
• Theorem 4.6 (Base Angle Theorem): If two
sides of a triangle are congruent then the
two angles opposite them are congruent.
• If AB ≅ AC  <B ≅ <C
In an Isosceles Triangle…..
• Theorem 4.6 (Conversed of Base Angle
Theorem): If two angles of a triangle are
congruent then the opposite side are
congruent.
• If <B ≅ <C  AB ≅ AC
Corollaries:
A proposition that follows with little or no proof required.
• Corollary to 4.6 Theorem: If a triangle is
equilateral (all sides are equal), then it is
equalangular (all angles are equal).
• Corollary to 4.7 Theorem: If a triangle is
equalangular, then it is equilateral.
Example #1
• Find x and y
• Δ 1 it equilateral (all 3 sides ≅)
equalangular (all 3 angles ≅)
Example #1
• Find x and y
• Δ 1 it equilateral equalangular
• all 3 sides ≅  all 3 angles ≅
Example #1
• Find x and y
• Δ 1 it equilateral equalangular
• all 3 sides ≅  all 3 angles ≅
Example #1
• Find x and y
• Δ 1 it equilateral
equalangular
• all 3 sides ≅  all 3
angles ≅
• x°+ x°+ x°=180°
• 3x°=180°
• X=60°
Example #1
• Find x and y
• Δ 1 it equilateral
equalangular
• all 3 sides ≅  all 3
angles ≅
• x°+ x°+ x°=180°
• 3x°=180°
• X=60°
Example #1
• Find x and y
• Δ 1 it equilateral
equalangular
• all 3 sides ≅  all 3
angles ≅
• x°+ x°+ x°=180°
• 3x°=180°
• X=60°
Example #1
•
•
•
•
•
Find x and y
Δ 2 is an isosceles
Therefore base angles are ≅
X=60°
180 – 60 = 120
Example #1
• Find x and y
• Δ 2 is an isosceles
• Therefore base
angles are ≅
• X=60°
• 180 – 60 = 120
• In Δ 2
120 +y° + y°=180
120 + 2y° = 180
-120
-120
2y° = 60
2
2
y = 30°
Example #1
• Find x and y
• Δ 2 is an isosceles
• Therefore base
angles are ≅
• X=60°
• 180 – 60 = 120
• In Δ 2
120 +y° + y°=180
120 + 2y° = 180
-120
-120
2y° = 60
2
2
y = 30°
Example #1
• Find x and y
• Δ 2 is an isosceles
• Therefore base
angles are ≅
• X=60°
• 180 – 60 = 120
• In Δ 2
120 +y° + y°=180
120 + 2y° = 180
-120
-120
2y° = 60
2
2
y = 30°
Example #1
• Find x and y
• Δ 2 is an isosceles
• Therefore base
angles are ≅
• X=60°
• 180 – 60 = 120
• In Δ 2
120 +y° + y°=180
120 + 2y° = 180
-120
-120
2y° = 60
2
2
y = 30°
Example #1
• Find x and y
• Δ 2 is an isosceles
• Therefore base
angles are ≅
• X=60°
• 180 – 60 = 120
• In Δ 2
120 +y° + y°=180
120 + 2y° = 180
-120
-120
2y° = 60
2
2
y = 30°
Theorem 4.8: Hypotenuse-Leg
Congruence Theorem (HL)
• If Hypotenuse and a leg of a right triangle
is congruent to hypotenuse and a leg of
second triangle  the two triangles are
congruent.
• If BC ≅ EF and AC ≅ DF  ΔABC ≅
ΔDEF
Example #2
• Find x and y
Example #2
• Find x and y
Example #2
• Find x and y
Example #3
• Decide whether the two triangles are ≅
according to the given information
Example #3
• Decide whether the two triangles are ≅
according to the given information
Example #3
• Decide whether the two triangles are ≅
according to the given information
Example #3
• Decide whether the two triangles are ≅
according to the given information
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