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Proving Triangles Congruent

Proving Triangles Congruent. Notes 19 – Sections 4.4 & 4.5. Essential Learnings. Students will understand and be able to use postulates to prove triangle congruence. Side-Side-Side (SSS) Congruence.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent Notes 19 – Sections 4.4 & 4.5

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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

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

  9. Angle-Angle-Angle (AAA) • Angle-Angle-Angle does not prove congruence.

  10. M Example 1 N Given: MN ≅ PN and LM ≅ LP Prove: LNM ≅ LNP. Statement Reason MN ≅ PN and LM ≅ LP Given LN ≅ LN Reflexive property LNM ≅ LNP By SSS P L

  11. Corresponding Parts of Congruent Triangles are Congruent (CPCTC) • Once you prove that triangles are congruent, you can say that “corresponding parts of congruent triangles are congruent (CPCTC).

  12. Example 2 W X Given: WX ≅ YZ and XW//ZY. Prove: ∠XWZ ≅ ∠ZYX. Statement Reason WX ≅ YZ and XW//ZY Given XZ ≅ ZX Reflexive property ∠WXZ ≅ ∠YZX Alt. Int. Angles (AIA) XWZ ≅ ZYX By SAS ∠XWZ ≅ ∠ZYX By CPCTC Y Z

  13. K J Example 3 L M Given: ∠NKL ≅ ∠NJM and KL ≅ JM Prove: LN≅ MN Statement Reason ∠NKL ≅ ∠NJM & KL ≅ JM Given ∠JNM≅ ∠KNL Reflexive property JNM ≅ KNL By AAS LN ≅ MN By CPCTC N

  14. B Example 4 – Flowchart Proof Given: ∠ABD ≅ ∠CBD and ∠ADB ≅ ∠CDB Prove: AB ≅ CB. ∠ABD ≅ ∠CBD Given ∠ADB ≅ ∠CDB Given BD ≅ BD reflexive prop. D A C ABD ≅ CBD by ASA AB ≅ CB by CPCTC

  15. Assignment Worksheet 4.4/4.5b Unit Study Guide 3

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