Triangle Congruence by SSS and SAS February 24, 2012

Warm-up  Practice Workbook p. 40, #1-10

Warm-up

Questions on Homework?

28.

Questions on Homework? 28.

Questions on Homework? 28.

Questions on Homework? 28.

Questions on Homework? 28.

Questions on Homework? 28.

Questions on Homework? 28.

Questions on Homework? 44.

Questions on Homework? 44.

Questions on Homework? 44.

Questions on Homework? 44.

Questions on Homework? 44.

Questions on Homework? 44.

Questions on Homework? 44.

Questions on Homework? 44.

Section 4-2 Triangle Congruence by SSS and SAS  Objectives: Today you will learn to prove triangles congruent using the SSS and SAS Postulates

Investigation  Congruence Applet: tail.aspx?ID=4  Each Triangle Congruence Postulate uses three elements (sides and angles) to prove congruence.  Today let’s investigate using Sides (2 or 3) and/or one Angle

Conclusions  In which configuration(s) were the triangles always congruent?  Side-Angle-Side (SAS)  Side-Side-Side (SSS)  In which configuration(s) were the triangles sometimes congruent?  Side-Side-Angle (SSA) – can’t use!

Which Postulate?

Side-Side-Side (SSS) Postulate If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. ΔGHF ≅ ΔPQR

Example: SSS Postulate Example 1: Prove ΔABD ≅ ΔCBD Given: ≅ segments as marked

Example: SSS Postulate Example 1: Prove ΔABD ≅ ΔCBD Given: ≅ segments as marked

Example: SSS Postulate Example 2: Prove ΔADE ≅ ΔCBE Given: ≅ segments as marked AC and BD bisect each other

Example: SSS Postulate Example 3: Prove ΔADC ≅ ΔBDC Given: ≅ segments as marked What else do we know? What else do you need to know?

Example: SSS Postulate Example 3: Prove ΔADC ≅ ΔBDC Given: ≅ segments as marked What else do we know? by Reflexive Property What else do you need to know? to prove by SSS

Side-Angle-Side (SAS) Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Side-Angle-Side (SAS) Postulate ΔCDE ≅ ΔFGH

Example: SAS Postulate Example 4: Prove ΔABD ≅ ΔCBD

Example: SAS Postulate Example 4: Prove ΔABD ≅ ΔCBD

Example: SAS Postulate Example 4: Prove ΔABD ≅ ΔCBD

Example: SAS Postulate Example 5: Prove ΔDFE ≅ ΔHFG

Example: SAS Postulate Example 5: Prove ΔDFE ≅ ΔHFG

Example: SAS Postulate Example 5: Prove ΔDFE ≅ ΔHFG

Example: SAS Postulate Example 6: Prove: ΔAEB ≅ ΔCED Given: The diagonal legs are joined at their midpoints

Example: SAS Postulate Example 6: Prove: ΔAEB ≅ ΔCED Given: The diagonal legs are joined at their midpoints

Example: SSS Postulate Example 7: Write the congruency statement.

Example: SSS Postulate Example 7: Write the congruency statement. ΔCAT ≅ ΔDOG ≅

Wrap-up  Today you learned to prove triangles congruent using the SSS and SAS Postulates  Tomorrow you’ll learn to prove triangles congruent using the ASA Postulate and the AAS Theorem Homework: pp. 189 – 192: 1-30, 33, 41-44