Question

Drag and drop the correct answer into each box to complete the proof.

Given: Rectangle ABCD

Prove: AC¯¯¯¯¯≅BD¯¯¯¯¯

Answer 1

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Answer 2

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

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).