Unit 2 check in - congruent triangles

​Congruence Statement

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​In the Figure, △ABC is congruent to △DEF. The symbol for congruence is ≅ and we write △ABC≅△DEF. ∠A corresponds to ∠D,  ∠B corresponds to ∠E, and ∠C corresponds to ∠F. Side AB corresponds to DE, BC corresponds to EF, and AC corresponds to DF.

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The Congruence Statement:  △ABC≅△DEF△ABC≅△DEF will always be written so that corresponding vertices appear in the same order, For the triangles in the figure we might also write △BAC≅△EDF, or △ACB≅△DFE but never for example △ABC≅△EDF nor △ACB≅△DEF.

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Therefore, we can always tell which parts correspond just from the congruence statement. For example, given that △ABC≅△DEF, side AB corresponds to side DE because each consists of the first two letters, AC corresponds to DF because each consists of the first and last letters, BC corresponds to EF because each consists of the last two letters.

 

Open Ended

Here are three triangles. Triangle PQR is congruent to which triangle? Explain your reasoning.

Multiple Choice

$$\Delta XYZ\cong\Delta TRS$$   Which side corresponds to side XY?

• TR

• RS

• ST

Multiple Choice

$$\Delta XYZ\cong\Delta TRS$$   Which side corresponds to side ZX?

• TR

• ST

• SR

Multiple Choice

Write the congruence statement. Triangle EFD is congruent to...

• Triangle TRS

• Triangle STR

• Triangle RST

Multiple Choice

Write the correct congruence statement.

$$\Delta ABC\cong$$  _________

• $$\Delta EDF$$  

• $$\Delta FED$$  

• $$\Delta EFD$$  

• $$\Delta DEF$$  

Multiple Choice

$$\Delta VUW\cong$$  ______

• $$\Delta ZYX$$  

• $$\Delta YXZ$$  

• $$\Delta XYZ$$  

• $$\Delta ZXY$$  

Triangle Conditions

Multiple Choice

Which of the following is NOT a valid way to show that two triangles are congruent?

• SSS

• SAS

• SSA

• ASA

Multiple Choice

Are these congruent? If so, provide a reason.

• Yes, SAS

• Yes, AAS

• Yes, ASA

• Not congruent

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SAS
• SSS
• ASA
• HL

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSS
• ASA
• AAS
• SAS

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• AAS
• SSS
• SAS
• SSA

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SAS
• Not enough information
• SSS
• AAS

Multiple Choice

• Congruent by HL
• Congruent by SAS
• Congruent by SSS
• Not Necessarily Congruent

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

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 conguent 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?

• No

• Yes