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Geometry
The Isosceles Triangle Theorems
Find the value of x.
1)
2)
3x-5
x + 21
40˚
x
40˚
70˚
3)
4)
16
x˚
3x – 2
100˚
5)
6)
70˚
64˚
x˚
x˚
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Write a Two Column Proof.
D
Given: AB ≅ CB, AD ≅ CD
7)
Prove: m∠BAD ≅ m∠BCD
A
1
3
2
4
C
B
A
8)
Given: AB ≅ AC , ∠B ≅ ∠2, ∠C ≅ ∠1,
Prove: ∆ADE is isosceles
D 1
2
B
E
C
C
9)
Given: BC ≅ DC , BF ≅ DE
Prove: ∠1 ≅ ∠2
1
B
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F
2
E
D
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Answer Key
1)
2)
3)
4)
5)
6)
x =13
x = 55
x=6
x = 20
x = 70
x = 64
AB ≅ CB, AD ≅ CD.......... Given
∠2 ≅ ∠4, ∠1 ≅ ∠3.......... Isosceles Triangle Theorem
7) m∠1 + m∠2 = m∠3 + m∠4 .......... Addition Property of Equality
m∠BAD = m∠1 + m∠2; m∠BCD = m∠3 + m∠4 .......... Angle Addition Postulate
m∠BAD = m∠BCD .......... Substitution
AB ≅ AC ......... Given
∠B ≅ ∠C .......... Isosceles Triangle Theorem
8)
∠B ≅ ∠2; ∠C ≅ ∠1 .......... Given
∠1 ≅ ∠2 .......... Substitution Property
AD ≅ AE .......... If two angles of a triangle are ≅ , then the sides opposite those angles are ≅
∆ADE is isosceles .......... Definition of Isosceles Triangle
9)
BC ≅ DC , BF ≅ DE ......... Given
∠B ≅ ∠D .......... Isosceles Triangle Theorem
∆CBF ≅ ∆CDE .......... SAS
∠1 ≅ ∠2.......... CPCTC
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