Download Postulate 4-2 Side-Angle-Side (SAS) Postulate

Triangle Congruence by SSS and SAS Notes
Name ________________________________________ Period _____ Date ________________
Objective: Students will prove two triangles are congruent using SSS and SAS Postulates in order
to find congruent triangles in a real-world connection
Warm-Up: Textbook Page 186 Numbers 1 – 3
If two triangles have three pairs of congruent corresponding angles and three pairs of congruent
corresponding sides, then the triangles are _________________________.
However, it is not necessary to know that all six corresponding parts are congruent in order to conclude that
two triangles are congruent. It is enough to know only that corresponding sides are congruent.
Postulate 4-1: Side-Side-Side (SSS) Postulate
If the ____________ ____________ of one triangle are
___________________ to the___________ ___________ of another
triangle, then the two triangles are _____________________.
(_________ Postulate)
If GH  ____ , HF  ____ , and GF  _____, then Δ_______  Δ________
Real-World
Connection
Bridge Design: The bridge girders are the same
size, as marked.
_____ ,
_____
Is this enough information to prove the two triangles are congruent? If so, write a flow proof.
Statement:
Reason:
AB 
AD 
_____________
______________
________________________________
Conclusion: Δ_______  Δ________
BD  BD
The word included is used frequently when referring to the angles and the sides of a triangle.
BX is included between ___ and
___ , while  N is included between ______ and ______.
Postulate 4-2 Side-Angle-Side (SAS) Postulate
If _______ ____________ and the __________________ _____________ of one
triangle are _____________________ to__________ sides and the
______________ angle of another triangle, then the two triangles are
________________________.
If BC  _____, CA  _______ and D   _____, then ΔBCA  Δ ___________. (________ Postulate)
Using SSS and SAS Postulates
Using ΔRSK and ΔTKS in the diagram shown, RS  _____ (_______________) and
SK  _____ (___________________________) , what other information is needed to
prove ΔRSK  ΔTKS using the SSS postulate? ________________
Using ΔRSK and ΔTKS in the diagram shown, RS  _____ (_______________) and
SK  _____ (___________________________) , what other information is needed to
prove ΔRSK  ΔTKS using the SAS postulate? ___________________
Are the Triangles Congruent?
Developing Proof: From the information given, can you prove RED
using SSS postulate or SAS postulate ? Explain.
RE  _____, RD  _____, and  R   _____
Group Activity: Textbook Page 191 Number 33
33. Developing Proof: Supply the reasons in this proof.
Given: X is the midpoint of AG and of NR. Prove: ΔANX > ΔGRX
Statements
Reasons
1. 1  2
a. ________________________
2. X is the midpoint of AG.
b. ________________________
3. AX  GX
c. ________________________
4. X is the midpoint of NR.
d. ________________________
5. NX  RX
e. ________________________
CAT
6. ΔANX  ΔGRX
f.________________________
Independent Activities: Class Work: Textbook Pages 189 - 191 Numbers 1 – 30
Homework: Textbook Page 192 Numbers 45 - 52