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Notes 19 – Sections 4.4 & 4.5 Students will understand and be able to use postulates to prove triangle congruence. If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent. 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. 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. 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. 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. Side-Side-Angle does not prove congruence. Angle-Angle-Angle does not prove congruence. M N Given: MN ≅ PN and LM ≅ LP Prove: LNM ≅ LNP. L Statement MN ≅ PN and LM ≅ LP LN ≅ LN LNM ≅ LNP Reason Given Reflexive property By SSS P Once you prove that triangles are congruent, you can say that “corresponding parts of congruent triangles are congruent (CPCTC). W Given: WX ≅ YZ and XW//ZY. Prove: ∠XWZ ≅ ∠ZYX. Statement WX ≅ YZ and XW//ZY XZ ≅ ZX ∠WXZ ≅ ∠YZX XWZ ≅ ZYX ∠XWZ ≅ ∠ZYX X Z Y Reason Given Reflexive property Alt. Int. Angles (AIA) By SAS By CPCTC K J Given: ∠NKL ≅ ∠NJM and KL ≅ JM Prove: LN ≅ MN Statement ∠NKL ≅ ∠NJM & KL ≅ JM ∠JNM ≅ ∠KNL JNM ≅ KNL LN ≅ MN L M N Reason Given Reflexive property By AAS By CPCTC B Given: ∠ABD ≅ ∠CBD and ∠ADB ≅ ∠CDB Prove: AB ≅ CB. A ∠ABD ≅ ∠CBD Given ∠ADB ≅ ∠CDB Given BD ≅ BD reflexive prop. ABD ≅ CBD by ASA D C AB ≅ CB by CPCTC Worksheet 4.4/4.5b Unit Study Guide 3