Lesson 4-2: Triangle Congruence – SSS, SAS, ASA, & AAS

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Triangle Congruence by SSS and SAS

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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 → ∆’s congruent by SSS (side-side-side) Rule

Draw the following figures using a ruler A triangle with a 900 angle. Measure only the 2 sides that touch the 900 Draw another triangle in a different “manner” using the 2 measured lengths and 900 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 other 2 sides and the included angle → ∆’s congruent by SAS (side-angle side) Rule → Look for SAS – list S or A in order 8 8 750 750 12 12

Examples 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. Y A P X B

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

Proving Congruence in ∆’s Go in a circle around triangle naming markings or measures in order (S or A) ∆’s congruent if : SSS : all 3 sides SAS : an angle between (included) 2 sides ASA : a side between 2 angles AAS : a side after 2 angles NEW ONES!

What are the letter combinations we can’t use? AAA A$$

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

Which side is included between R and F in ∆FTR? 2. Which angles in ∆ STU include ? 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. 3. 4. 5. Q H G P I R P L Quiz Tomorrow! 4-1, 4-2 4-3 Y A A B C X