G.6 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.

Multiple Select

Classify the triangle shown in the picture by its SIDES.

• Isosceles

• Obtuse

• Equilateral

• Scalene

Multiple Choice

measure of Angle H=

• 38

• 71

Fill in the Blanks

Multiple Choice

FD =

• KI

• IK

• JK

• KJ

Multiple Choice

Angle A = ?

• L

• M

• N

Multiple Choice

ANGLE U = ANGLE ?

• E

• F

• G

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

SAS=Side Angle Side Postulate

• SAS: states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

ASA: Angle Side Angle Postulate

• ASA: states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

AAS: Angle Angle Side Postulate

• AAS: states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

SSS: Side Side Side

• SSS: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Congruence of sides is shown with little hatch marks, like this: ∥. For two triangles, sides may be marked with one, two, and three hatch marks.

HL: Hypotenuse Leg Postulate

• HL: The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

CPCTC: Corresponding Parts of Congruent Triangles are Congurent

• CPCTC: is an acronym for corresponding parts of congruent triangles are congruent.

Writing a Proof

Statements/Reasons 

Multiple Choice

How are triangle ABC and triangle A'B'C' Congruent?

• SAS

• AAS

• ASA

• HL

Multiple Choice

How would you prove triangle MPN and triangle RSQ are congruent?

• ASA

• SSS

• SAS

• CPCTC

Multiple Choice

How would prove triangle ABC and triangle DEF are congruent?

• SSS

• AAS

• HL

• CPCTC

Multiple Choice

Which of the following cannot be used to prove triangles are congruent?

• ASA
• SSA

• SSS
• SAS

Multiple Choice

What are the five ways to prove triangles are congruent?

• SSS, ASA, AAS, SAS, HL
• SSS, SSA, HL, AAS, SAS
• SAS, SSA, HL, AAS, SSS
• HL, SAS, SSA, SSS, ASA

Multiple Choice

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

• SAS
• ASA
• AAS
• Not Possible

Multiple Choice

Congruent by

• SSS
• SAS
• ASA
• AAS

Multiple Select

Are the two triangles congruent? If they are, select the correct congruence theorem. If there is not enough information, select N/A.

• ASA

• SSA

• SAS

• N/A

Multiple Choice

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

• SAS
• ASA
• AAS
• Not Possible

Multiple Choice

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

• SSS
• SAS
• ASA
• AAS

Multiple Choice

What is always the 1st statement in the reason column of a proof?

• Prove
• Given
• Reason
• Statement

Multiple Choice

What reason would I put for statements 1, 2,3, 4

• reflexive property

• definition of congruence

• given

• definition of midpoint

• vertical angles are congruent

Multiple Choice

What would be the correct "given" statements for this diagram?

• T is the midpoint of segment BG and
  ∡B≅∡G
• ∡B≅∡G and ∡A≅∡W
• T is the midpoint of segment BG and ∡A≅∡W
• T is the midpoint of segment AW and ∡A≅∡W

Multiple Choice

Fill in the blank.

• Given
• Reflexive Property
• Transitive Property
• They're the same side!!!!!! 

Multiple Choice

Fill in the missing proofs.

• Transitive Property, SAS(Side-Angle-Side)
• Reflexive Property, SAS(Side-Angle-Side)
• Reflexive Property, Vertical Angles Thm.
• Transitive Property, SSS(Side-Side-Side)