Download Isoceles And Equilateral Triangles

Aim: What theorems apply to isosceles and
equilateral triangles?
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Do Now:
Given: AKC is isosceles with KA  KC
KB bisects AKC
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Prove: A  C
Statements
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C
Reasons
1) KA  KC
2) KB bisects AKC
1) Given
2) Given
3) AKB  CKB
3) Def. angle bisector
4) KB  KB
5) AKB  CKB
4) Reflexive Postulate
5) SAS  SAS
6) A  C
6) Corr. parts of  ' s are1 
Theorem
: Theorem:
Isosceles Triangle
The Base angles of an isosceles triangle are congruent.
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D
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Corollary : The bisector of the vertex angle of an
isosceles triangle bisects the base.
Corollary :
The bisector of the vertex angle of an
isosceles triangle is perpendicular to the base.
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In other words: The median, altitude and angle bisector from
the vertex of an isosceles triangle are all the same segment.
Equilateral Triangles
Corollary : Every equilateral triangle is equiangular.
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B
B
Or
A
A  C
C
Or
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A  B
B
C
A  B  C
C
A
B  C
C
Ex: Isosceles Triangles
If the following pairs of segments are
congruent, which angles are congruent.
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1) LD  LK Ans: D  K
2) QL  QT Ans : QTL  QLT
3) QT  FT Ans : TQF  TFQ
4) FL  TL Ans : LFT  LTF
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D
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Algebra w/Isosceles Triangles
Isosceles ABC has AB  AC. If AB  8 x  8,
AC  6 x  38, and BC  3x  24 determine AB,
AC and BC.
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Ex: Proof w/Isosceles Triangle
Given: Isosceles VRK with VR  VK
M is the midpoint of RK
TMR  AMK
Prove: MT  MA
Statements
A
T
R
M
K
Reasons
1) VR  VK
2) R  K
1) Given
2) Base 's of isosc. 's are  .
3) M is the midpoint of RK 3) Given
4) MR  MK
5) TMR  AMK
TMR  AMK
7) MT  MA
6)
4) Def. Of midpoint
5) Given
6) ASA  ASA
7) Corr. parts of  ' s are 6
Geometry Lesson: Isosceles and
Equilateral Triangle Theorems
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Proofs w/Isosceles Triangles
1) Given: Isosceles RDV with RD  RV
Isosceles TDV with TD  TV
Prove: RDT  RVT
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2) Given: Isosceles MGD with MG  MD
y
GHTD , x  y
Prove: MHT is isosceles
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3) Given: Isosceles ALE with AL  AE
QL  NE , PQ  AL, PN  AE
Prove: QPL  NPE
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