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1. Prove that the three angle bisectors of a triangle concur.

§ 4.1. C. A. B. 1. Prove that the three angle bisectors of a triangle concur. D. E. I. F. C. A. B. l 1. l 2. 2. Prove that the perpendicular bisectors of a triangle concur. O. l 3. U. T. C. Q. P. O. A. B. V. R. 3. Prove that the altitudes of a triangle concur.

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1. Prove that the three angle bisectors of a triangle concur.

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  1. § 4.1 C A B 1. Prove that the three angle bisectors of a triangle concur. D E I F

  2. C A B l1 l2 2. Prove that the perpendicular bisectors of a triangle concur. O l3

  3. U T C Q P O A B V R 3. Prove that the altitudes of a triangle concur. Note that the altitudes of ∆ABC are the perpendicular bisectors of the sides of ∆PQR and using the previous problem the perpendicular bisectors concur.

  4. B 4. Complete the proof that the exterior angle of a triangle is greater than each of its remote interior angles. D E C A Given: A – C – D and ∆ ABC Prove  ACG >  A G F

  5. 6. Given: AD bisects  CAB and CA = CD. Prove: CD parallel to AB.

  6. 7. Segments AB and CD bisect each other at E. Prove that AC is parallel to BD. B E C D A

  7. 8. Given two lines cut by a transversal. If a pair of corresponding angles are congruent, prove that a pair of alternate interior angles are congruent. Given: l and m cut by transversal m and  A =  B. t Prove:  A =  C. B l C A m

  8. 9. Given two lines cut by a transversal. If a pair of corresponding angles are congruent, prove that the lines are parallel. Given: l and m cut by transversal m and  A =  B. t Prove: l and m parallel. B l C A m

  9. 11. Given triangle ABC with AC = BC and DC = EC, and  EDC =  EBA, prove DE is parallel to AB. Given: AC = BC and DC = EC, and  EDC =  EBA Prove: DE is parallel to AB.

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