Download S.s.A. Theorem (for obtuse ∆`s) Side-Side

S.s.A. Theorem (for obtuse ∆’s)
BIG SIDE-small side-ANGLE THEOREM:
If one angle (∠HLS) and two consecutive sides (SH & HL) of one triangle (∆LHS)
are congruent to one angle (∠WTO) and two consecutive sides (OW & WT) of another (∆TWO),
and the larger of the two congruent sides (SH > HL) are opposite the congruent angles,
then the triangles are congruent.
S
O
≅
L
GIVEN:
∠SLH ≅ ∠OTW,
SH = OW > LH = TW,
obtuse ∆’s LHS & TWO,
∆TWO ≅ ∆RHS
S
H
H
1
STATEMENTS
L
W
3
∆LHR is isosceles
4
T
Construct auxiliary
∆RHS ≅ ∆TWO,
then...
PROVE:
∆LHS ≅ ∆RHS
... to show
∆TWO ≅ ∆LHS.
2
REASONS
Isosceles ∆ Definition
R
m∠3 = m∠4
Isosceles ∆ Theorem
m∠1 = m∠2
Definition of Congruence
m∠SLR = m∠1 + m∠3
Angle Addition Postulate
m∠SLR = m∠2 + m∠4
Substitution Property
m∠4 + m∠2 = m∠LRS
Angle Addition Postulate
m∠SLR = m∠LRS
Transitive Property
LS = RS
Isosceles ∆ Converse
∆LHS = ∆RHS
Side-Side-Side