Question

Jimmy wrote the following proof to show that the diagonals of rectangle ABCD are congruent:

Jimmy's Proof:
Statement 1: Rectangle ABCD is given.
Statement 2: Segment AB ≅ Segment DC because opposite sides of a rectangle are congruent.
Statement 3: Angles ABC and DCB are both right angles by definition of a rectangle.
Statement 4: Angles ABC and DCB are congruent because all right angles are congruent.
Statement 5: ________________________________.
Statement 6: Triangles ABC and DCB are congruent by SAS.
Statement 7: Segment AC ≅ Segment DB by CPCTC.
Option 1: Segment AB ≅ Segment CD
Option 2: Segment BC ≅ Segment AD
Option 3: Segment AC ≅ Segment BD
Option 4: Angles ABC and ABD are congruent.

Answer 1

Jimmy's proof is missing statement 5. The missing statement should be 'Segment AC is congruent to Segment BD by the definition of a rectangle's diagonals.'

Step-by-step explanation:

Jimmy's Proof:

1. Rectangle ABCD is given.
2. Segment AB ≅ Segment DC because opposite sides of a rectangle are congruent.
3. Angles ABC and DCB are both right angles by definition of a rectangle.
4. Angles ABC and DCB are congruent because all right angles are congruent.
5. Segment AC ≅ Segment BD by definition of a rectangle's diagonals.
6. Triangles ABC and DCB are congruent by SAS.
7. Segment AC ≅ Segment DB by CPCTC.