Download Guided Notes - Proving Triangle Congruence with ASA and AAS

Geometry
Name: __________________________________
Guided Notes
Proving Triangle Congruence Using ASA and AAS
Date: ______________________ Period: ______
(ASA)__________________________________________________- If two angles and the
included side of one triangle are congruent to two angles and the included side of a second
triangle, then the two triangles are congruent.
If angle ∡A ≅ __________,
side ̅̅̅̅ ≅
, and
angle ∡C ≅ __________,then
ΔABC ≅ ΔDEF
(AAS) _________________________________________________- If two angles and a nonincluded angle of one triangle are congruent to two angles and a non-included angle of a
second triangle, then the two triangles are congruent.
If angle ∡A ≅ __________,
angle ∡C ≅ __________, and
side ̅̅̅̅ ≅
, then
ΔABC ≅ ΔDEF
ASA______________________________________Not ASA_________________________
AAS______________________________________Not AAS_________________________
Geometry
Name: __________________________________
Guided Notes
Proving Triangle Congruence Using ASA and AAS
Date: ______________________ Period: ______
(HL) If the __________________________________________________ are congruent to the
hypotenuse and leg of a second right triangle, then the two triangles are congruent.
Example #1: Is it possible to prove that the triangles are congruent? If so, state the postulate of
theorem you would use.
Example #2: Identify which property will prove these triangles congruent.
Example #3: State the third congruence that must be given to prove that ΔABC ≅ ΔDEF using the
indicated postulate or theorem.
Geometry
Name: __________________________________
Guided Notes
Proving Triangle Congruence Using ASA and AAS
Date: ______________________ Period: ______
Example #4: Decide whether enough information is given to prove that the triangles are congruent. If
there is enough information, state the congruence postulate you would use.
ΔXYW, ΔZWY
ΔMAE, ΔTAE
Example #5:
Given: ̅̅̅̅̅
̅̅̅̅ ∡Y ≅ ∡X
Prove: ∆WYZ ≅ ∆ZXW
Statements
Justifications
ΔDKA, ΔTKS
Geometry
Guided Notes
Proving Triangle Congruence Using ASA and AAS
Example #6:
Given: ̅̅̅̅
̅̅̅̅
̅̅̅̅
Name: __________________________________
Date: ______________________ Period: ______
̅̅̅̅
Prove: ∆ABC ≅ ∆DCB
Statements
Justifications
Example #7:
Given: ̅̅̅̅ ⊥ ̅̅̅̅ ; ̅̅̅̅ ⊥ ̅̅̅̅
C is the midpoint of ̅̅̅̅
Prove: ∆ABC ≅ ∆DEC
Statements
Justifications