D. Copy and complete each two-column proof. 1. Given: ST I TY, DY ITY, SY = DT Prove: SU = DU PROOF Statements Reasons 1. ST L TY DY L TY SY = DT 2. ZSTY and ZDYT are 2. right angles. 3. 3. Definition of right triangles 4. Reflexive Property of Segment Congruence 5. ASTY = ADYT 5. 6. ZS= LD, ST = DY 6. 7. LSUT= 8. ASTU = ADYU 2|Page 2. The median to the base of an isosceles triangle is the perpendicular bisector of the base. Restatement: Given: Isosceles triangle ABC with AC = BC and median CD Prove: CD is the perpendicular bisector of AB PROOF Statements Reasons 1 . AC = BC 1. Median CD of AABC . D is the midpoint of AB. 2. 3. 3. Definition of midpoint 4. LA = LB 4. 5. ACAD = ACBD 5. 6. ZCDA = LCDB 6. 7. ZCDA and ZCDB form 7. a linear pair 8. 8. Linear Pair Postulate 9. 9. Theorem 3.1 10. CD is perpendicular to 10. Definition of perpendi- AB cular segments 11. 11. O E