Answer:
Statement Reason
1. Rectangle ABCD Given
2. AD=BC Opposite sides of a rectangle are congruent
3. DC=DC Reflexive Property of Congruence
4. <ADC and <BCD are Definition of rectangle
right angles
5. <ADC=<BCD All right angles are congruent
6. ∆ADC=∆BCD SAS Congruence Postulate
7. AC=BD CPCTC
Step-by-step explanation:
2. AD=BC because the opposite sides of a rectangle are congruent.
3. DC=DC, each segment is equal to itself because the Reflexive Property of Congruence.
4. <ADC and <BCD are right angles because the interior angle of any rectangle are right angles (Definition of rectangle).
5. <ADC=<BCD, because they are right angles and all right angles are congruent.
6. ∆ADC is congruent with ∆BCD because the have two congruent sides (AD with BC and DC with DC), and congruent the angle between these sides (<ADC with <BCD): Side Angle Side Congruence Postulate (SAS Congruence Postulate).
7. AC must be congruent with BD because Congruent Parts in Congruent Triangles must be Congruent (CPCTC).
