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Question

Use the image to answer the question.

Prove that the diagonals of rectangle LMNO
are congruent. You can write a two-column proof or a paragraph proof, but be sure to include a reason for each of your statements.

(4 points)

Short Answer Rubric (4 points)

Answer 1

To prove that the diagonals of rectangle LMNO are congruent, we can use a two-column proof format.

Two-Column Proof:

| Statement | Reason | |---------------------------------------------|----------------------------------------------| | 1. Rectangle LMNO is given. | 1. Given | | 2. Opposite sides of a rectangle are equal: LM = ON and LO = MN. | 2. Definition of a rectangle | | 3. Triangles LMO and ONM are formed by the diagonals. | 3. Diagonals connect opposite corners | | 4. LM = ON (opposite sides of the rectangle) | 4. Property of rectangles | | 5. LO = MN (opposite sides of the rectangle) | 5. Property of rectangles | | 6. Diagonal LN is common to both triangles LMO and ONM. | 6. Common side in both triangles | | 7. Triangles LMO and ONM are congruent by the Side-Side-Side (SSS) Postulate. | 7. SSS Congruence Theorem | | 8. Therefore, diagonal LN is congruent to diagonal OM. | 8. Corresponding parts of congruent triangles are congruent | | 9. Diagonal LO is congruent to diagonal MN. | 9. Same reasoning as above |

Conclusion: Since we have shown that the diagonals LN and OM of rectangle LMNO are congruent through congruent triangles, we can conclude that the diagonals of any rectangle are congruent. This is a fundamental property of rectangles.