Download Congruent Polygons, SAS Postulate

Aim: What are congruent polygons? How do we prove
triangles congruent using Side-Angle-Side Postulate?
A
Do Now:
Given: AD bisects BAC
12
3 is complementary to 1
4 is complementary to 2
4 C
B 3
Prove: 3  4
D
Statement
Reason
1) AB bisects BAC 1)Given
2) 3 compl. 1
2)Given
3) 4 compl. 2
3)Given
4) 1  2
4)Def. angle bisector
5) 3  4
5)Complements of the same or
congruent
angles are congruent.1
Geometry Lesson: Congruent
Polygons, Triangles, SAS
Def: Congruent Polygons
Two polygons are congruent if and only if:
a) Corresponding angles are congruent.
b) Corresponding sides are congruent.
B
C Polygon ABCD  Polygon EFGH
A
D
F
G
E
A  E
B  F
C  G
D  H
AB  EF
BC  FG
CD  GH
DA  HE
H
Geometry Lesson: Congruent
Polygons, Triangles, SAS
2
Ex: Congruent Polygons
M 50º 96º H
1) Given the triangles shown:
34º
a) Write a congruence statement for
the triangles. BHM  QRA
b) Which angle is congruent to H? R
R
A
96º
50º
34º
B
Q
c) Which side is congruent to side AQ? MB
2)Given that TNF  JSG :
a)Which angle is congruent to SGJ ? NFT
b)Which angle is congruent to NTF ? SJG
c)Which side is congruent to TN ? JS
d)Which side is congruent to GJ ? FT
Geometry Lesson: Congruent
Polygons, Triangles, SAS
3
Postulate: Side-Angle-Side Postulate (SAS)
Postulate:
If two sides and the included angle of one triangle are
congruent to two sides and the included angle of another
triangle, then the two triangles are congruent.
There
is onlyan
one
length for
the 3rdusing
side that will
Construct
identical
triangle
complete
theand
triangle.
two sides
the included angle.
Ex: Which pairs of triangles can be proved
congruent using S-A-S?
1)
x
2)

3)
X
Geometry Lesson: Congruent
Polygons, Triangles, SAS
X
4
Ex 1: Proof w/S.A.S.
Given: CD bisects ACB
AC  BC
Prove: ACD  BCD
Statement
1) CD bisects ACB
2) AC  BC (s)
3) 1  2 (a)
4) CD  CD
(s)
5) ACD  BCD
C
1 2
A
D
B
Reason
1)
2)
3)
4)
5)
Given
Given
Def. angle bisector
Reflexive Postulate
S.A.S. Postulate
Geometry Lesson: Congruent
Polygons, Triangles, SAS
5
Ex 2,3,4: Proofs w/S.A.S.
2) Given: AE  BC , E  C
D is midpoint of EC
Prove: ADE  BDC
3) Given: AC bisects EB at D
EB bisects AC at D
Prove: AED  CBD
4) Given: BPD , AP  CP
x  y
Prove: ABP  CBP
A
B
E
A
C
D
B
E
D
A
B
Geometry Lesson: Congruent
Polygons, Triangles, SAS
x
P y
C
D
C
6