Post on 30-Dec-2015
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4.4 – Prove Triangles Congruent by SAS
Geometry Ms. Rinaldi
Included Angles
The included angle is the angle between two sides.
Side-Angle-Side (SAS) Congruence Postulate
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.
If Side
Angle
Side
Then
RSAB
A
B
C
R
S
T
TRCA
RSTABC
RA
EXAMPLE 1 Use SAS
Decide whether the congruence statement is true. Explain your reasoning.
DEFABC
SOLUTION DFAC
FECB FC
(S)
(A)
(S)
So, by SAS, DEFABC
EXAMPLE 2 Use SAS
Decide whether the congruence statement is true. Explain your reasoning.
DFRNJH
SOLUTION
Although there are two pairs of congruent sides, the congruent angles are not included (between) the congruent sides.
Therefore SAS does not apply and the triangles are not congruent.
EXAMPLE 3 Use SAS
Decide whether the congruence statement is true. Explain your reasoning.
ERFEPF
Hint: This is possible! Do not forget the side they both share!
EXAMPLE 4 Use SAS
Decide whether the congruence statement is true. Explain your reasoning.
GTSPTF
Hint: This is possible! You have the sides, you only need a pair of congruent angles in between…
EXAMPLE 5 Use SAS
Decide whether the congruence statement is true. Explain your reasoning.
CDAABC
Hint: This is possible! Look for alternate interior angles as well as a side that both triangles share.
EXAMPLE 6 Use SAS and properties of shapes
In the diagram, QS and RP pass through the center M of the circle. What can you conclude about MRS and MPQ?
SOLUTION
Because they are vertical angles, PMQ RMS. All points on a circle are the same distance from the center, so MP, MQ, MR, and MS are all equal.
MRS and MPQ are congruent by the SAS Congruence Postulate.
ANSWER
EXAMPLE 7 Use SSS or SAS
State the third congruence that must be given to prove that using the indicated postulate.DEFABC
A
B
C
D
E
F
Given:
Use the SSS Congruence Postulate.
DEAB FECB
SOLUTION
To use SSS, you need to know that DFAC
EXAMPLE 8 Use SSS or SAS
State the third congruence that must be given to prove that using the indicated postulate.DEFABC
A
B
C
D
E
F
Given:
Use the SAS Congruence Postulate.
DA FDCA
SOLUTION
To use SAS, you need to know that EDBA
EXAMPLE 9 Use SSS or SAS
State the third congruence that must be given to prove that using the indicated postulate.DEFABC
A
B
C
D
E
F
Given:
Use the SAS Congruence Postulate.
EB DEAB