Download SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs

Isosceles Triangles
November 4, 2011
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
QUIZ
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
HW ANSWERS
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
HW ANSWERS
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
HW ANSWERS
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
HW ANSWERS
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
HW ANSWERS
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
CB
∡B
Def. of Isosceles ∆
A
CA
∡A
S
AM
BM
Def of midpoint
∆ADM
∆BEM
SAS (3, 5, 6)
CPCTC
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
1 2
Given
∡A
A
∡EAP
S
AP
∡1
A
∡B
∡DBP
BP
∡2
Subtraction Post. (2,3)
Vertical
s
ASA (4, 5, 6)
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Given
CD
∡1
CE
∡2
Subtraction Post (1,2)
SWBAT: Use the Isosceles Triangle Theorem
Plan: ∆ADC
C
∆BEC
31
2 4
SS
∡1
A
∡2
∡1 is suppl to ∡3
∡2 is suppl to ∡4
∡3 ∡4
ADC
BEC
SAS (1, 5, 1)
AC
CPCTC
BC
Linear Pair Thm
B
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Plan: ∆CEA
∆CDB
S
DE
AE
∡CEA
CEA
DE
BD S
∡CDB A
CDB
Addition Post (1,2)
SAS (1, 4, 3)
CPCTC
SWBAT: Use the Isosceles Triangle Theorem in Triangle Proofs
Plan: ∆BAC
∡D
∆EFD
∡C
DC
DC
AC
FD
BC
ED
BAC
EFD
∡B
∡E
Addition Post (3,4)
SAS (5, 2, 6)
CPCTC