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.
To prove that the diagonals of rectangle LMNO are congruent, we will use the definition of a rectangle and properties of rectangles.
Statement | Reason
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1. Rectangle LMNO is a rectangle. | Given.
2. LMO is a right angle. | Definition of a rectangle.
3. LNO is a right angle. | Definition of a rectangle.
4. Triangle LMO is a right triangle. | Definition of a right angle.
5. Triangle LNO is a right triangle. | Definition of a right angle.
6. LM = MO. | By definition of a rectangle, opposite sides are congruent.
7. LN = NO. | By definition of a rectangle, opposite sides are congruent.
8. Triangle LMO is congruent to triangle LNO. | By hypotenuse-leg congruence theorem, since LM = LN, MO = NO, and triangle LMO and LNO have a right angle in common.
9. OM = ON. | By corresponding parts of congruent triangles LMO and LNO, the hypotenuse (or diagonal) is congruent in both triangles.
From statement 6 (LM = MO) and statement 9 (OM = ON), we can conclude that the diagonals of rectangle LMNO (OM and ON) are congruent.