Transcript Ways to Prove Triangles Congruent

Ways to Prove
Triangles Congruent
HL Method
4 Known Methods
Side – Angle – Side
 Angle – Side – Angle
 Angle – Angle – Side
 Side – Side – Side


PLUS ONE MORE!!!
Hypotenuse-Leg
(HL Method)
•
Only works with a right triangle
• Must have a right angle
• Hypotenuses must be congruent
• Must also have one additional
side (leg)
Must both have right angles,
congruent legs and congruent
hypotenuses.
Example of HL Method
* Would otherwise have been SSA except for the right angle.
Corresponding Parts of
Congruent Triangles are
Congruent
(CPCTC)
After we prove two triangles congruent, there are 6
corresponding parts that are therefore congruent, 3
sides and 3 angles.
CPCTC often used in proofs
Given: BO=MA
OW=AN
BW=MN
Prove: ∠O=∠A
Statements
Reasons
BO=MA
Given
OW=AN
Given
BW=MN
Given
∆BOW=∆MAN
SSS Method of Congruence
∠O=∠A
CPCTC