Three Ways to Prove Triangles

Prove Triangle Congruence

Criteria for Proving that two triangles are congruent

Instead of having to prove all three sides and all three angles are ≌, we have combinations of sides and angles that will work to prove triangles are ≌

SSS

• All three pairs of corresponding sides are congruent

• All three sides have to marked as congruent

• or

• The triangles have to share a common side (reflexive property)

Multiple Choice

Does SSS prove the Triangles congruent?

• No, only two pairs of sides is marked as congruent

• Yes, all three sides are congruent because of reflexive property

Multiple Choice

Does SSS prove the triangles are congruent?

• No, only two sides are marked as congruent

• Yes, we can use reflexive property to mark the third side congruent

SAS

Two sides are congruent

and

The included angles are congruent

(included angle means between between the two congruent sides)

Multiple Choice

Does SAS prove the triangles are congruent?

• Yes

• NO

Multiple Choice

Does SAS work to prove the triangles are congruent?

• No, there are no congruent angles

• Yes, two sides are congreunt and the included angle is congruent because they are vertical angles

Remember, vertical angles are ALWAYS CONGRUENT

So, when you see them mark them as congruent.

ASA

• Two pair of congruent ANGLES

• One pair of congruent included sides (included side means side between the two angles)

Multiple Choice

Does ASA work to prove the triangles are congruent?

• No, there is only one pair of congruent angles

• Yes, the second pair of congruent angles are the vertical angle

Multiple Choice

Does ASA work to prove the triangles are congruent?

• Yes, the reflexive side is congruent, so you have 2 angles and a included side

• No, you only have to angles. You need an included side

AAS

Two congruent angles

and

A non-included side (the congruent sides are not between the congruent angles)

Multiple Choice

Does AAS work to prove the triangles are congruent?

• Yes

• NO

HL (Hypotenuse Leg)

Used with right ∆'s only

One leg is marked a congruent

and

the hypotenuse is marked as congruent

Multiple Choice

Does HL work to prove the triangles are congruent?

• Yes

• No

Assignment

#19 Qt. 4 Worksheet!

Due Monday at the beginning of class for full credit!