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Isosceles Triangles
November 12, 2015
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Warm - Up
5
∡1  ∡4, 𝑋𝑃 ≅ 𝑇𝑌
A
S
A
∡1 is suppl to ∡2,
∡3 is suppl to ∡4
∡2  ∡3
6
Given
Linear Pair Thm
𝑋𝑅 ≅ 𝑌𝑅
Mdpt  2  segments
𝑃𝑅 ≅ 𝑇𝑅
∡5  ∡6
Subtraction Post. (5,1)
∆PQR  ∆TSR
ASA (4, 6, 7)
9 𝑃𝑄 ≅ 𝑇𝑆
Vertical s are 
9 CPCTC
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Isosceles Triangle
Theorem
If two sides of a triangle are congruent,
then the angles opposite those sides
are congruent.
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Converse of Isosceles
Triangle Theorem
If two angles of a triangle are
congruent, then the sides opposite
those angles are congruent.
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Plan: ∆ADM  ∆BEM by SAS
Given
S
A
CA  CB
∡A  ∡B
S
AM  BM
∆ADM  ∆BEM
Mdpt  2  segments
SAS (3, 5, 6)
CPCTC
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
1 2
Given
∡A  ∡B
A
∡EAP  ∡DBP
Subtraction Post. (3,2)
S
AP  BP
∡1  ∡2
Vertical s are 
A
ASA (4, 5, 6)
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Given
CD  CE
∡1  ∡2
Subtraction Post (1,2)
SWBAT: Use the Isosceles Triangle Theorem
C
Plan: ∆ADC  ∆BEC
31
2 4
SS
∡1  ∡2
A
∡1 is suppl to ∡3
∡2 is suppl to ∡4
Linear Pair Thm
∡3  ∡4
ADC  BEC
SAS (1, 5, 1)
AC  BC
CPCTC
B
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Plan: ∆CEA  ∆CDB
S
DE  DE
AE  BD S
Addition Post (1,2)
∡CEA  ∡CDB A
CEA  CDB
SAS (1, 4, 3)
CPCTC
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Plan: ∆BAC  ∆EFD
A
S
S
∡BCA  ∡EDF
DC  DC
AC  FD
BC  ED
BAC  EFD
∡B  ∡E
Addition Post (3,4)
SAS (5, 2, 6)
CPCTC
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs