Download 3.7 Angle Side Theorems

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Transcript
3.7 Angle Side Theorems
Theorem 20: Isosceles Triangle
Theorem (ITT)
 If 2 sides of a triangle are congruent, then the
angles opposite the sides are congruent.
A
A
If
then
B
C
B
C
Theorem 21: Converse Isosceles
Triangle Theorem (CITT)
 If 2 angles of a triangle are congruent, then
the sides opposite the angles are congruent.
A
A
If
then
B
C
B
C
Can you prove theorems 20 &21?
 ITT can be proven using SSS by naming the
triangle in a correspondence with itself.
 CITT can be proven using ASA by naming the
triangle in a correspondence with itself.
 Special Note: for triangles, equilateral and
equiangular will be used interchangeably.
Given:
D
E  H
EF  HG
Prove:
DF  DG
Statements
1.
E  H
Reasons
1.
Given
EF  HG
2.
DE  DH
3. DEF  DHG
4.
DF  DG
2. CITT
If
3.
SAS
4.
CPCTC
E
then
F
G
H
Given:
XY  XZ
Prove:
1  2
X
1
Y
Statements
1.
XY  XZ
2
Z
Reasons
1.
Given
2.
XYZ  XZY
2.
If
2. ITT
3.
1 is suppl. to XYZ
3. If 2 angles form a straight line, then
2 is suppl. to XZY
4.
1  2
then
they are supplementary
4.
If 2 angles are supplementary to
4. ST
congruent angles then they are
congruent
More Practice Proofs
More Practice Proofs