answer to ch 6 proofs

3. Given: KA = KL;NE || KL .NKProve: ∆ ANE is isoscelesSTATEMENTSAREASONSEL1. KA = KL 1. Given2. ∠ A = ∠ L 2. = sides in ∆ opposite ∠ ’s =3. NE || KL 3. Given4. ∠ NEA, ∠ L are corresponding ∠ ’s 4. def. corresponding angles5. ∠ NEA = ∠ L 5. Parallel lines corresponding ∠ ’s =6. ∠ NEA = ∠ A 6. Substitution/transitive (2 5)7. NA = NE 7. = ∠ ’s in ∆ opposite sides =8. ∆ ANE is isosceles 8. Equal sides isosceles ∆S4. Given: ∆ ASE and ∆ AGE are right triangleswith right angles S and G; AS = GEProve: SE || AGAEGSTATEMENTSREASONS1. ∆ ASE and ∆ AGE are right triangles 1. Givenwith right angles S and G; AS = GE2. AE = AE 2. Reflexive Prop. =3. ∆ ASE ≅ ∆ EGA 3. HL (#1, 1, 2)4. ∠ SEA = ∠ GAE 4. CPCTE5. ∠ SEA, ∠ GAE are alt. int ∠ ’s 5. def. alternate interior angles(transversal AE )6. SE || AG 6. Alt. interior ∠ ’s = parallel lines