Download Definition of ≅ ∆`s Definition of Midpoint Isosceles ∆ Vertex Thms

GEOMETRY
∆ Proofs
S.s.A. Theorem
NAME_________________________
DATE __________ Per.___________
S.s.A. THEOREM (for Right ∆’s):
If one angle (∠LHS) and two consecutive sides (LS & SH) of one triangle (∆LHS)
are congruent to one angle (∠TWO) and two consecutive sides (TO & OW) of another (∆TWO),
and the larger of the two congruent sides (LS > SH) are opposite the congruent angles,
then the triangles are congruent.
S
O
≅
L
GIVEN:
SL = OT > SH = OW,
right ∆’s LHS & TWO,
∆TWO ≅ ∆RHS
L
STATEMENTS
H
W
S
3
4
1
2
H
T
Construct auxiliary
∆RHS ≅ ∆TWO,
then...
PROVE:
∆LHS ≅ ∆RHS
... to show
∆TWO ≅ ∆LHS.
R
REASONS
∆RSL is isosceles
Isosceles ∆ Definition
∠L ≅ ∠R
Isosceles ∆ Theorem
∠1 and ∠2 are right
Definition of Right ∆’s
∠1 ≅ ∠2
Right Angle Theorem
∠3 ≅ ∠4
Third Angle Theorem
HS ⊥ LR
⊥ Lines Converse/Def.
H is midpoint of LR
Isosceles ∆ Vertex Thms.
LH = HR
Definition of Midpoint
∆LHS ≅ ∆RHS
Definition of ≅ ∆’s