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Triangles Congruency Theorems

Triangles Congruency Theorems. Notes 18 – Sections 4.4 & 4.5. Essential Learnings. Students will understand and be able to use postulates to prove triangle congruence. Vocabulary. Included angle – the angle formed by two adjacent sides of a polygon.

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Triangles Congruency Theorems

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  1. Triangles Congruency Theorems Notes 18 – Sections 4.4 & 4.5

  2. Essential Learnings • Students will understand and be able to use postulates to prove triangle congruence.

  3. Vocabulary • Included angle – the angle formed by two adjacent sides of a polygon. • Included side – the side located between two consecutive angles of a polygon.

  4. Side-Side-Side (SSS) Congruence • If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.

  5. Example 1 Given: GH ≅ KL, HL ≅ JL, and L is the midpoint of GK. Congruence Statement: GHL ≅ ________ by _______ H J G K L

  6. Side-Angle-Side (SAS) Congruence • If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

  7. Side-Side-Angle (SSA) • Side-Side-Angle does not prove congruence.

  8. Angle-Side-Angle (ASA) Congruence • If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.

  9. Angle-Angle-Side (AAS) Congruence • If two angles and the non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the triangles are congruent.

  10. Angle-Angle-Angle (AAA) • Angle-Angle-Angle does not prove congruence. 60° 60° 60° 60° 60° 60°

  11. Hypotenuse-Leg (HL) Congruence • If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

  12. Example 2 Given: ∠DAB and ∠DCB are right angles and AB ≅ CB Congruence Statement: _______ ≅ _______ by ________ B C A D

  13. Example 3 Given: MN ≅ PN and LM ≅ LP Congruence Statement: _______ ≅ _______ by ________ M N P L

  14. Example 4 Given: WX ≅ YZ and WX//YZ. Congruence Statement: _______ ≅ _______ by ________ W X Y Z

  15. Example 5 Given: ∠NKL ≅ ∠NJM and KL ≅ JM Congruence Statement: _______ ≅ _______ by ________ J K O L M N

  16. Example 6 Given: ∠ABD ≅ ∠CBD and ∠ADB ≅ ∠CDB Congruence Statement: _______ ≅ _______ by ________ B D A C

  17. Assignment Worksheet 4.4/4.5(a) Math’s Mates Quiz – next Wednesday Unit Study Guide 3

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