Notes 19 – Sections 4.4 & 4.5

SStudents will understand and be able to use postulates to prove triangle congruence.

IIf three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.

I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.

I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.

I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.

I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.

SSide-Side-Angle does not prove congruence.

AAngle-Angle-Angle does not prove congruence.

Given: MN ≅ PN and LM ≅ LP Prove:  LNM ≅  LNP. StatementReason MN ≅ PN and LM ≅ LPGiven LN ≅ LNReflexive property  LNM ≅  LNPBy SSS N M L P

OOnce you prove that triangles are congruent, you can say that “corresponding parts of congruent triangles are congruent (CPCTC).

Given: WX ≅ YZ and XW//ZY. Prove: ∠XWZ ≅ ∠ZYX. StatementReason WX ≅ YZ and XW//ZYGiven XZ ≅ ZXReflexive property ∠WXZ ≅ ∠YZXAlt. Int. Angles (AIA)  XWZ ≅  ZYXBy SAS ∠XWZ ≅ ∠ZYXBy CPCTC W Z X Y

Given: ∠NKL ≅ ∠NJM and KL ≅ JM Prove: LN ≅ MN StatementReason ∠NKL ≅ ∠NJM & KL ≅ JMGiven ∠JNM ≅ ∠KNLReflexive property  JNM ≅  KNLBy AAS LN ≅ MNBy CPCTC J L N K M

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

Worksheet 4.4/4.5b Unit Study Guide 3