Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS Vocab SSS (side-side-side) congruence Included angle SAS (side-angle-side) congruence

Draw the following figures using a ruler Draw a triangle, measure its lengths Draw another triangle in a different “manner” using the same length sides. Are the 2 triangles different? Are they the same shape, same size? They’re Congruent!

SSS congruence If 3 sides are congruent to other 3 sides →

Draw the following figures using a ruler A triangle with a 90 0 angle. Measure only the 2 sides that touch the 90 0 Draw another triangle in a different “manner” using the 2 measured lengths and 90 0 angle between them Are the 2 triangles different? Are they the same shape, same size? They’re Congruent!

SAS congruence If 2 sides and the included angle between them are congruent to corresponding parts → → Look for SAS – list S or A in order

Examples 1.In ∆VGB, which sides include B? 2. In ∆STN, which angle is included between and ? 3. Which triangles can you prove congruent? Tell whether you would use the SSS or SAS Postulate. A B P X Y

4. What other information do you need to prove ∆DWO ∆DWG? 5. Can you prove ∆ SED ∆BUT from the information given? Explain. D OG W D E S B U T

Proving Congruence in ∆’s Go in a circle around triangle naming markings or measures in order (S or A) ∆’s congruent if : –SSS : –SAS : –ASA : –AAS :

What are the letter combinations we can’t use?

Hints Use facts/rules to find any missing angle or side measures first –Is a side congruent to itself? –Can you use any angle facts to find missing angle measures? –Look for parallel lines

6.Which side is included between R and F in ∆ FTR? 7.2. Which angles in ∆ STU include ? 8.Tell whether you can prove the triangles congruent by ASA or AAS. If you can, state a triangle congruence and the postulate or theorem you used. If not, write not possible. P Q R G H I P L A Y A BC X