Congruent Triangles

Congruent Triangles

Part 1

Open Ended

What information would you need to prove two triangles are congruent?

Congruent Triangles

Triangles are congruent if corresponding angles and sides are congruent.

Congruent Statements

The statements are used to show what corresponding parts are congruent

Congruent Triangles

How can this congruency be stated?

Fill in the Blanks

If

 $\Delta JKL\ \cong\ \Delta COT$ , finish the congruent statements.
 $JK\ \cong\ ?$ ,  $?\ \cong\ CT$  ,  $KL\ \cong\ ?$  

To state two triangles are congruent, we only need 4 postulates to help us determine triangle congruent

• Side-Side-Side

• Side-Angle-Side

• Angle-Side-Angle

• Angle-Angle-Side

Side-Side-Side Congruency (SSS)

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Open Ended

Determine if Angle-Angle-Angle Congruency (AAA) exits and explain why or why not.

Side-Angle-Side Congruency (SAS)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of the second triangle, then the two triangles are congruent.

Open Ended

Determine if Side-Side-Angle Congruency exits, explain why or why not.

Fill in the Blanks

What information is needed to prove the triangles congruent by SSS? Write out the statement.

Fill in the Blanks

What information is needed to prove triangles congruent by SAS? Write out the congruent statement.

What information is needed to prove the triangles are congruent by SSS?

AC is congruent to ES because it is given. SC is congruent to CS by reflexive property. Therefore the needed information would be AS congruent to EC.

Consider Triangle CAR & Triangle CER.

Let's fill in the proof

Consider Triangle GRT & Triangle ARE

Let's fill in the proof.

Fill in the Blanks

Determine if the triangles can be proven congruent by either SSS or SAS and if so, what information is needed. If not, explain.

Multiple Choice

Which of the reasons for statement 5 is correct?

• AAA

• SAS

• SSS

• Can't prove congruency