Download Find the value of x. and triangles. 1.

Find the value of x.
1.
2.
3. Write the congruent statements for the sides, angles,
and triangles.
Geometry
5.3/5.5 Proving Triangles Congruent
Essential Question
What can you conclude about two triangles
when you know certain parts are congruent?
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Goals
Use SSS and SAS theorems postulates to
prove triangles are congruent.
 Solve triangle problems.

December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Congruent Triangles
Congruent triangles are the same shape
and same size.
 There are three pairs of congruent sides.
 There are three pairs of congruent angles.

C
ABC  RST
B
A
December 7, 2015
T
R
5.3 Proving Triangles Congruent: SSS, SAS
S
BUT…

To prove two triangles are congruent you
don’t need to prove that the three sides
and three angles are congruent.
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Side-Side-Side Theorem (SSS)
If three sides of one triangle are congruent
to three sides of another triangle, then the
triangles are congruent.
B
S
ABC  RST
A
December 7, 2015
C
R
5.3 Proving Triangles Congruent: SSS, SAS
T
Are these triangles congruent?
YES!
S
S
S
S
10
12
12
10
7
S
December 7, 2015
7
S
Why? SSS
5.3 Proving Triangles Congruent: SSS, SAS
Prove MAD  MAN.
A
N
M
D
Reasons
Statements
1. 𝑀𝐷  𝑀𝑁
2. 𝐴𝐷  𝐴𝑁
1. Given
2. Given
3. 𝐴𝑀  𝐴𝑀
4. MAD  MAN
3. Reflexive
December 7, 2015
4. SSS
5.3 Proving Triangles Congruent: SSS, SAS
Included Angle
B
For adjacent sides AB and AC,
A is the included angle.
C
A
For sides BC and BA, what is
the included angle? B
For sides CB and CA, what is
the included angle? C
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Example 1
Name the included angle.
M
T
a. 𝑀𝑇 and 𝑇𝑅
R
MTR or RTM
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Q
Example 1
Name the included angle.
M
T
b. 𝑇𝑄 and 𝑅𝑇
RTQ or QTR
December 7, 2015
R
5.3 Proving Triangles Congruent: SSS, SAS
Q
Now You Try
T
M
R
a. 𝑅𝑇 and 𝑀𝑅
b. 𝑇𝑄 and 𝑅𝑄
c. 𝑀𝑅 and 𝑇𝑀
d. 𝑅𝑇 and 𝑄𝑅
December 7, 2015
MRT or TRM
TQR or RQT or Q
RMT or TMR or M
TRQ or QRT
5.3 Proving Triangles Congruent: SSS, SAS
Q
Example 2
Name the pairs of corresponding angles and
corresponding sides.
ABC  TDF
A  T
B  D
C  F
December 7, 2015
AB  TD
BC  DF
AC  TF
5.3 Proving Triangles Congruent: SSS, SAS
Your Turn
Name the pairs of corresponding angles and
corresponding sides.
DCT  FLG
D  F
C  L
T  G
December 7, 2015
𝐷𝐶 ≅ 𝐹𝐿
𝐶𝑇 ≅ 𝐿𝐺
𝐷𝑇 ≅ 𝐹𝐺
5.3 Proving Triangles Congruent: SSS, SAS
Another way to show s 
Side-Angle-Side
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
SAS Theorem
If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent.
B
A
N
C
M
ABC  MNP
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
P
Example 3
Are these triangles congruent?
10 cm
10 cm
50°
50°
25 cm
25 cm
Yes by SAS.
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Example 4
Are these triangles congruent?
A
S
8
S
12
80°
70°
30°
S8
80°
A
Yes, by SAS.
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
12 S
SSA: Side-Side-Angle
THIS DOES NOT WORK!
 It is a very common trap and students fall
for it easily.
 Example: are these triangles congruent?

S
S
A
S
December 7, 2015
NO!
A
S
5.3 Proving Triangles Congruent: SSS, SAS
SSA
Why doesn’t it work?
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Why doesn’t it work?
These triangles are not congruent
even though two sides and an angle
are congruent.
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Your Turn
For the next six problems, decide whether
there is enough information given to prove
the triangles are congruent. If there is
enough information, state the theorem you
would use.
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Your Turn 1
Decide whether there is enough information given
to prove the triangles are congruent. If there is
enough information, state the theorem you would
use.
X
 by SSS
S
S
S
W
December 7, 2015
Y
5.3 Proving Triangles Congruent: SSS, SAS
S
S
Z
Your Turn 2
Decide whether there is enough information given
to prove the triangles are congruent. If there is
enough information, state the theorem you would
use.
E
Not  (uses SSA)
M
A
S
S
A
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
S
A
T
Your Turn 3
Decide whether there is enough information given
to prove the triangles are congruent. If there is
enough information, state the theorem you would
L
use.
S
 by SAS
K
A
S
A
J
S
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
H
Your Turn 4
Decide whether there is enough information given
to prove the triangles are congruent. If there is
enough information, state the theorem you would
use.
 by SAS
A
S
S
S
A KA
S
S
D
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
T
Your Turn 5
Decide whether there is enough information given
to prove the triangles are congruent. If there is
enough information, state the theorem you would
use.
E
L
S
S
Not  (uses SSA)
N
December 7, 2015
A
S
V
5.3 Proving Triangles Congruent: SSS, SAS
A S
O
Your Turn 6
Decide whether there is enough information given
to prove the triangles are congruent. If there is
enough information, state the theorem you would
use.
 by SSS
S
S
S
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
S
S
Summary
To prove two triangles are congruent use
or
December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Caution!
When using SAS make sure the angle is
between the two adjacent sides.
 SSS is the easiest to use.

December 7, 2015
5.3 Proving Triangles Congruent: SSS, SAS
Assignment
B
B
A
C
SAS
December 7, 2015
A
SSS
5.3 Proving Triangles Congruent: SSS, SAS
C