Triangle Congruency Theorems

​This means that all 3 sides are congruent.

​​Side-Side-Side

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​This means the 2 sides are congruent as well as the angle between them. (Order matters)

​​Side-Angle-Side

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​This means the 2 angles are congruent as well as the side between them. (Order matters)

​​Angle-Side-Angle

​This means the 2 angles are congruent as well as the side beside (not between) one of the angles. (Order matters)

​​Angle-Angle-Side

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​There are 4 Triangle Theorems that are used to prove that triangles are congruent.

​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.

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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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​Important information:

• Before you can state the congruent triangle theorem, you have to identify which parts are congruent. All we know is the we have 2 parallel lines and line JL is the transversal.

  • ∠MJL ≅​ ∠KLJ (Angle) -> They are alternate interior angles (single markings)

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

  • ∠MLJ ≅​ ∠KJL (Angle) -> They are alternate interior angles (double markings)

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

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​Get each to a 50. 50 = 100 ~ Due Tuesday