Geo 4.5: Congruent Triangles SSS & SAS

1. Tell if and why the triangles are congruent. Not congruent, not enough info ∡A ≅ ∡C, thus ∆'s are ≅ by SAS ∆≅ Thm. . ∆'s are ≅ by the definition of ≅∆'s A B D C 2. Tell if and why the triangles are congruent. Not congruent, not enough info AB ≅ CB, thus ∆'s are ≅ by SSS ∆≅ Thm. BD ≅ BD, thus ∆'s are ≅, by SAS ∆≅ Thm. ∆'s are ≅ by the definition of ≅∆'s A B D C 3. Tell what the value x must be in order for the two triangles to be congruent by SSS ∆ ≅ Thm. 6x - 4 B x = A C 4x + 7 D 4. Tell if and how the two triangles are congruent. C A Not congruent, not enough info AC ≅ED, thus ∆'s are ≅ by SSS ∆≅ ∡ABC ≅∡EBD, thus ∆'s are ≅ by SAS ∆≅ B D E 5. Which additional information is needed to prove ΔABC ≅ ΔCDE by SAS Δ ≅ theorem? A C E B ∡B ≅ ∡D AB ∕∕ CD CB ≅ ED D 6. What additional information is needed to prove ΔABC ≅Δ EBD by SSS Δ ≅ theorem? B is the midpoint of CD AC ∕∕ ED C A B AC ≅ ED ∡CBA ≅ ∡DBE D E 7. Which congruence theorem or definition would you use to prove these triangles congruent? SSS Δ ≅ theorem W definition of ≅ Δ's S O SAS Δ ≅ theorem N Not enough information to prove triangles congruent ? Tell which statement is true for the following pairs of triangles. Triangles congruent by SAS ∆≅ Thm. ? Congruent triangles by SSS ∆≅ Thm. ? 9. Could you use SSS or SAS to prove ΔSNO ≅ ΔOWS? W S YES NO O N 10. Tell if and how the two triangles are congruent. C A Not congruent, not enough info AB ≅ EB, thus ∆'s are ≅ by SSS ∆≅ AB ≅ EB and AC ≅ ED, thus ∆'s are ≅ by SSS ∆≅ B D E Congruent by SSS∆≅ Thm. ? Identify which statement is true for each of the pairs of triangles below. Congruent by SAS ∆≅Thm. ? Not enough info to prove triangles congruent. ? What additional information is needed to prove these triangles are congruent by SAS ∆≅ Thm. RS ≅ PQ RO ≅ OQ ∡P ≅ ∡S ∡R ≅ ∡Q Complete the proof by dragging the correct statements and reasons to their locations. Prove: ∆QAB ≅ ∆PBA ∆QAB ≅ ∆PBA ? ∡QAB ≅ ∡PBA Statements AQ ≅ BP ? AB ≅ AB Reflexive Property of ≅ ? SAS ∆ ≅ Thm. ? Given Given ? Reasons not used: SSS ∆≅ Thm. ? |

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