Using Direct Proofs to Prove Triangles Congruent
Using Direct Proofs to Prove Triangles Congruent Problem Set
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Given: E is the midpoint of AD and BC.
Prove: △AEB ≅ △DEC
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. -
Given: GF ≅ JF, and H bisects GJ.
Prove: △GFH ≅ △JFH
Statement Reason 1. GF ≅ JF 1. 2. H bisects GJ. 2. 3. GH ≅ JH 3. 4. FH ≅ FH 4. 5. △GFH ≅ △JFH 5. -
Given: △ALT and △TSA are right triangles, and LT ≅ SA.
Prove: △ALT ≅ △TSA
Statement Reason 1. △ALT and △TSA are right triangles. 1. 2. LT ≅ SA 2. 3. AT ≅ AT 3. 4. △ALT ≅ △TSA 4. -
Given: ED bisects ∠BDC, and ∠B ≅ ∠C.
Prove: △BED ≅ △CED
Statement Reason 1. ED bisects ∠BDC. 1. 2. ∠B ≅ ∠C 2. 3. ∠BDE ≅ ∠CDE 3. 4. ED ≅ ED 4. 5. △BED ≅ △CED 5. -
Given: ∠E ≅ ∠H, and I is the midpoint of EH.
Prove: △EIF ≅ △HIG
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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