Prove that the diagonals of rectangle LMNO are congruent. Use the Drag and drop to fill out the proof below.
1. Response area is a rectangle 1. Given
2. LMNO is a Response area. 2. All rectangles are parallelograms
3. LO¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯ 3. Opposite sides of a Response area are congruent
4. ∠LON and ∠MNO are right angles 4. Definition of a Response area
5. Response area 5. Right Angle Congruence Theorem
6. Response area 6. Reflexive Property of Congruence
7. △LON≅△MNO 7. Response area
8. LN¯¯¯¯¯¯¯¯≅MO¯¯¯¯¯¯¯¯¯ 8. Respond area
8. Diagonals of a rectangle bisect each other, so LN¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯████MO¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ (Segment Addition Postulate)
9. LN¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯≅MO¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ (Definition of Congruent Segments)