4.3 – prove triangles congruent by sss. we know… triangles have six parts but do we really need...
TRANSCRIPT
4.3 – Prove Triangles Congruent by SSS
• We know…
Triangles have six parts
But do we really need all six parts to say two triangles are congruent?
Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
If Side
Side
Side
Then
RSAB
A
B
C
R
S
T
STBC
TRCA RSTABC
EXAMPLE 1 Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning.
NLKL
NMKM
SOLUTION
NLMKLM
LMLM
Given
Given
Reflexive Property
So, by the SSS Congruence Postulate,
NLMKLM
EXAMPLE 2 Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning.
ACB CAD
It is given that BC AD By Reflexive propertyAC AC, But AB is not congruent CD. Therefore, the triangles are not congruent.
SOLUTION
EXAMPLE 3 Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning.
DFG HJK
EXAMPLE 4 Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning.
A B
CD
CDBABD
EXAMPLE 5 Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning. A
B
CD
CDBABD
EXAMPLE 6 Use the SSS Congruence Postulate
has vertices J(-3, -2), K(0, -2), and L(-3, -8).
has vertices R(10, 0), S(10, -3), and T(4, 0).
Graph the triangles in the same coordinate plane and show that they are congruent.
SOLUTION
KJ = SR = 3. (By counting)
JL = RT = 6. (By counting)
LK = TS =6.7 (By distance formula)
Use the distance formula to find the lengths of the diagonal segments.
7.645)6()3())2(8()03( 2222 LK
7.645)3()6())3(0()104( 2222 TS
Therefore, by SSS, the triangles are congruent.
JKLRST
EXAMPLE 7 Use the SSS Congruence Postulate
has vertices P(-5, 4), Q(-1, 4), and R(-1, 1).
has vertices A(2, 5), B(2, 1), and C(5, 1).
Graph the triangles in the same coordinate plane and show that they are congruent.
STEP 1: Graph
PQ =_____ = _____ (By_____________)
QR = _____ = _____ (By ____________)
PR = _____ =______ (By ______________)
STEP 2: Use the distance formula to find the lengths of the diagonal segments.
PQR
ABC
PR =
AC =
Therefore, by ______, _________________________.