CONGRUENT TRIANGLES

CONGRUENT TRIANGLES

Let's do this!!

What makes a congruent triangle?

Remember that the word CONGRUENT means same size. We want to be able to say and prove that two triangles are congruent.

How do we know if 2 triangles are congruent?

• We have to prove that each SIDE in one triangle is congruent to the corresponding side in the other triangle.

• We have to prove that each ANGLE is congruent to the corresponding angle in the other triangle.

• When 2 triangles are congruent all the sides and all the angles are congruent.

Given 2 congruent triangles we know 6 things.

•  $\Delta ABC\cong\Delta DEF$  

• AB = DE

• AC = DF

• BC = EF

•  $\angle A\cong\angle D$  

•  $\angle B\cong\angle E$  

•  $\angle C\cong\angle F$  

Multiple Select

Classify the triangle shown in the picture by its SIDES.

• Isosceles

• Obtuse

• Equilateral

• Scalene

Draw a scalene triangle.

• Now we are going to draw another triangle congruent to it.

• If you have spaghetti noodles use them.

• You need 2 pieces one length, 2 pieces another length and 2 pieces the 3rd length.

• Make your two triangles. Are they the same size?

• They should be!

• If all sides of one triangle are congruent to all the sides of another triangle the triangles are congruent by Side-Side-Side Postulate, (SSS)

Multiple Choice

What does SSS stand for?

• Small Small Small
• Side Side Side
• Small Side Small
• Sam's Silly Side

Multiple Choice

What does SSS prove?

• Nothing
• Triangles similar
• Triangles congruent
• Triangle angle sum

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• ASA
• Not Possible

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS
• SAS
• AAS
• Not Possible

If 2 sides and the included angle of one triangle are congruent to the corresponding sides and angle of another triangle the triangles are congruent.

This is called Side Angle Side (SAS)

Multiple Choice

State if the two triangles are congruent. If they are, state which theorem you would use.

• Yes, SAS

• Yes, SSS

• No

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS

• SAS

• Not Possible

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS

• SAS

• Not possible

Multiple Choice

Name the postulate, if possible, that makes the triangles congruent.

• SSS

• SAS

• Not Possible

Multiple Choice

• Congruent by SSS

• Congruent by SAS

• Not Necessarily Congruent

Did I get you?

Remember the angle is included that means it is between the two congruent sides.

Today you learned about 2 triangle congruencies out of the 5.

SAS - Side Angle Side

SSS - Side-Side-Side

Time to practice!