Download Side-Side-Side Isosceles ∆ Converse Subtraction Property

BIG SIDE-small side-ANGLE THEORE
GEOMETRY
∆ Proofs
S.s.A Theorem (for acute ∆’s):
If one angle (∠HLS) and two consecutive sides (LS & SH) of one triangle (∆LHS)
are congruent to one angle (∠WTO) and two consecutive sides (TO & OW) of another (∆TWO),
and the larger of the two congruent sides (SH > LS) are opposite the congruent angles,
then the triangles are congruent.
H
GIVEN:
L
∠HLS ≅ ∠WTO,
SH = OW > SL = OT,
acute ∆’s LHS & TWO,
∆TWO ≅ ∆RHS
L
≅
W
H
O
S
T
1
2
4
3
STATEMENTS
∆LSR is isosceles
S
Construct auxiliary
∆RHS ≅ ∆TWO,
then...
PROVE:
∆LHS ≅ ∆RHS
... to show
∆TWO ≅ ∆LHS.
R
REASONS
Isosceles ∆ Definition
m∠3 = m∠4
Isosceles ∆ Theorem
m∠HLS = m∠WTO = m∠HRS
Congruence Definitions
m∠HLS = m∠1 + m∠3 Angle Addition Postulate
m∠HRS = m∠2 + m∠4 Angle Addition Postulate
m∠1+m∠3 = m∠2+m∠4
Substitution Property
m∠1 = m∠2
Subtraction Property
LH = RH
Isosceles ∆ Converse