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