Side Side Side Triangle Congruency

​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • Segment GH ≅​ Segment JI (Side) -> This is given to us by the single markings on each line.

  • We also know that Segment JH ≅ Segment JH (Side)because they are the same line.

  • Lastly, since GH and JI are parallel, we know that ∠GHJ ≅​ ∠IJH (Angle) because they are alternate interior angles. (**we have not learned about Alt. Int Angles yet, but I want you to get the general idea of the proof thought process)

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Therefore, since 2 sides are congruent and the angle between them is congruent, this is Side-Angle-Side

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​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • Segment PQ ≅​ Segment PS (Side) -> This is given to us by the single markings on each line.

  • Segment QR ≅​ Segment SR (Side) -> This is given to us by the double markings on each line.

  • We also know that Segment PR ≅ Segment PR (Side) because they are the same line.

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Therefore, since all 3 sides are congruent, this is Side-Side-Side!

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​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • ∠B ≅​ ∠D (Angle) -> This is given to us by the square marking the right angle.

  • Segment BC ≅​ Segment DC (Side) -> This is given to us by the single markings on each line.

  • We also know that ∠ACB ≅ ∠ECD (Angle) because they are vertical angles and vertical angles are ALWAYS congruent.

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Therefore, this is Angle-Side-Angle since that is the order of congruence!

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​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent.

  • ∠C ≅​ ∠F (Angle) -> This is given to us by the single marking the right angle.

  • ∠CED ≅​ ∠FED (Angle) -> This is given to us by the double markings on each line.

  • We also know that Segment DE ≅ Segment DE (Side) because they are the same line.

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Therefore, this is Angle-Angle-Side since that is the order of congruence!

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Multiple Choice

If ∆CAB≅∆FED , then $$\angle C\cong\angle F$$  

• True

• False

Multiple Choice

If ∆LMK ≅ ∆LMT, then ∠K ≅ ____ 

• $$L$$  

• $$\angle L$$  

• $$\angle T$$  

• T

Multiple Choice

If $$\Delta MAN\cong\Delta BOY$$ , which of the following statements are true?

• $$\overline{MA}\cong\overline{BO}$$  

• $$\overline{AN}\cong\overline{BY}$$  

• $$\overline{BO}\cong\overline{NA}$$  

• $$\overline{MN}\cong\overline{BO}$$  

Multiple Choice

Which of the following is not a postulate use to prove triangle congruence?

• SSA

• SAS

• ASA

• SSS

Multiple Choice

What is reason #4? #9

• ASA

• SAS

• HL

• AAS

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
• Not enough information given
• ASA

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

Which is not a postulate to prove triangle congruence?

• AAA

• ASA

• SSS

• SAS

Multiple Choice

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

• SSS

• SAS

• ASA

• NONE

Multiple Choice

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