aim:
DESCRIPTION
Aim:. What are congruent polygons? How do we prove triangles congruent using Side-Angle-Side Postulate?. A. Do Now:. Given:. 1. 2. 3. 4. B. Prove:. C. D. Given. Given. Given. Def. angle bisector. Complements of the same or congruent angles are congruent. B. F. C. G. A. E. - PowerPoint PPT PresentationTRANSCRIPT
1Geometry Lesson: Congruent Polygons, Triangles, SAS
Aim: What are congruent polygons? How do we prove triangles congruent using Side-Angle-Side Postulate?
Do Now:
21
3 4
A
B CD
Given:
Prove:
bisects AD BAC3 is complementary to 1 4 is complementary to 2
3 4
Statement Reason
1) 1)
2) 2)
3) 3)
4) 4)
5) 5)
bisects AB BAC
3 compl. 1 4 compl. 2 1 2 3 4
Given
Given
Given
Def. angle bisectorComplements of the same or congruent angles are congruent.
2Geometry Lesson: Congruent Polygons, Triangles, SAS
Def: Congruent PolygonsTwo polygons are congruent if and only if:
a) Corresponding angles are congruent.
b) Corresponding sides are congruent.
A
B C
D
E
F G
H
Polygon Polygon ABCD EFGH
A
B
C
D
E
F
G
H
AB
BC
CD
DA
EF
FG
GH
HE
3Geometry Lesson: Congruent Polygons, Triangles, SAS
Ex: Congruent Polygons
50º96º
34ºA
R
Q
96º
34º
50ºM H
B
1) Given the triangles shown:
a) Write a congruence statement for the triangles.
b) Which angle is congruent to H?
c) Which side is congruent to side AQ?
2)Given that :
a)Which angle is congruent to ?
b)Which angle is congruent to ?
c)Which side is congruent to ?
d)Which side is congruent to ?
TNF JSG
SGJ
NTF
TN
GJ
BHM QRA
R
MB
NFTSJG
JS
FT
4Geometry Lesson: Congruent Polygons, Triangles, SAS
Postulate: Postulate: Side-Angle-Side Postulate (SAS)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.
Construct an identical triangle using two sides and the included angle.
There is only one length for the 3rd side that will complete the triangle.
x
Ex: Which pairs of triangles can be proved congruent using S-A-S?
1) 2) 3)
X X
5Geometry Lesson: Congruent Polygons, Triangles, SAS
Ex 1: Proof w/S.A.S.
Statement Reason
1) 1)
2) 2)
3) 3)
4) 4)
5) 5)
GivenGiven
Def. angle bisector
Reflexive Postulate
S.A.S. Postulate
1 2
A B
C
D
Given:
Prove:
bisects CD ACBAC BCACD BCD
bisects CD ACB (s)AC BC
1 2 (a)
(s)CD CDACD BCD
6Geometry Lesson: Congruent Polygons, Triangles, SAS
Ex 2,3,4: Proofs w/S.A.S. A B
CDE
2) Given:
Prove:
AE BC , E C is midpoint of D ECADE BDC
A
B
C
DE
3) Given:
Prove:
bisects at DAC EB bisects at DEB AC
AED CBD
4) Given:
Prove:
BPD��������������
, AP CPx y
ABP CBP P
A
B
C
Dxy