Application
Using Direct Proofs to Prove Triangles Congruent

Using Direct Proofs to Prove Triangles Congruent Problem Set

  1. Given: E is the midpoint of AD and BC.
    Prove: △AEB ≅ △DEC
    figure 1
    Statement Reason
     1. E is the midpoint of AD and BC.  1.
     2. AE ≅ DE  2.
     3. BE ≅ CE  3.
     4. ∠AEB ≅ ∠DEC  4.
     5. △AEB ≅ △DEC  5.

    2.  

  2. Given: GF ≅ JF, and H bisects GJ.
    Prove: △GFH ≅ △JFH
    figure 2
    Statement Reason
     1. GF ≅ JF  1.
     2. H bisects GJ.  2.
     3. GH ≅ JH  3.
     4. FH ≅ FH  4.
     5. △GFH ≅ △JFH  5.

    3.  

  3. Given: △ALT and △TSA are right triangles, and LT ≅ SA.
    Prove: △ALT ≅ △TSA
    figure 3
    Statement Reason
     1. △ALT and △TSA are right triangles.  1.
     2. LT ≅ SA  2.
     3. AT ≅ AT  3.
     4. △ALT ≅ △TSA  4.

    4.  

  4. Given: ED bisects ∠BDC, and ∠B ≅ ∠C.
    Prove: △BED ≅ △CED
    figure 4
    Statement Reason
     1. ED bisects ∠BDC.  1.
     2. ∠B ≅ ∠C  2.
     3. ∠BDE ≅ ∠CDE  3.
     4. ED ≅ ED  4.
     5. △BED ≅ △CED  5.

    5.  

  5. Given: ∠E ≅ ∠H, and I is the midpoint of EH.
    Prove: △EIF ≅ △HIG
    figure 5
    Statement Reason
     1. ∠E ≅ ∠H  1.
     2. I is the midpoint of EH.  2.
     3. EI ≅ HI  3.
     4. ∠EIF ≅ ∠HIG  4.
     5. △EIF ≅ △HIG  5.


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