#### Transcript Notes 19 - Proving Triangles Congruent

### 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 Given: MN ≅ PN and LM ≅ LP Prove: LNM ≅ LNP.

Statement MN ≅ PN and LM ≅ LP LN ≅ LN LNM ≅ LNP N L 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 X Given: WX ≅ YZ and XW//ZY.

Prove: ∠XWZ ≅ ∠ZYX.

Statement WX ≅ YZ and XW//ZY XZ ≅ ZX ∠WXZ ≅ ∠YZX XWZ ≅ ZYX ∠XWZ ≅ ∠ZYX Z Reason Given Reflexive property Alt. Int. Angles (AIA) By SAS By CPCTC Y

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

B Given: ∠ABD ≅ ∠CBD and ∠ADB ≅ ∠CDB Prove: AB ≅ CB.

∠ABD ≅ ∠CBD Given ∠ADB ≅ ∠CDB Given BD ≅ BD reflexive prop.

ABD ≅ by ASA CBD A D C AB ≅ CB by CPCTC

Worksheet 4.4/4.5b

Unit Study Guide 3