Transcript Glencoe Geometry - Burlington County Institute of Technology

6.4
Rectangles
You used properties of parallelograms and
determined whether quadrilaterals were
parallelograms.
• Recognize and apply properties of
rectangles.
• Determine whether parallelograms are
rectangles.
• Rectangle:
a parallelogram with four right angles
**Remember a parallelogram has:
• Opposite sides parallel and congruent
• Opposite angles congruent
• Consecutive angles supplementary
• Diagonals bisect each other
Theorem 6.13: Diagonals of a Rectangle #1
If a parallelogram is a rectangle, then its
diagonals are congruent.
Theorem 6.14: Diagonals of a Rectangle #2
If the diagonals of a parallelogram are
congruent, then the parallelogram is a
rectangle.
**(Converse of Theorem 6.13)
Use Properties of Rectangles
CONSTRUCTION A rectangular garden gate is
reinforced with diagonal braces to prevent it from
sagging. If JK = 12 feet, and LN = 6.5 feet, find KM.
Answer: KM = 13 feet
Use Properties of Rectangles
Quadrilateral EFGH is a rectangle. If GH = 6 feet
and FH = 15 feet, find GJ.
Answer: GJ= 7.5 feet
Use Properties of Rectangles and Algebra
Quadrilateral RSTU is a rectangle. If mRTU =
8x + 4 and mSUR = 3x – 2, find x.
Proving Rectangle Relationships
ART Some artists stretch their own canvas over
wooden frames. This allows them to customize the
size of a canvas. In order to ensure that the frame is
rectangular before stretching the
canvas, an artist measures the
sides and the diagonals of the
frame. If AB = 12 inches,
BC = 35 inches, CD = 12 inches,
DA = 35 inches, BD = 37 inches,
and AC = 37 inches, explain how
an artist can be sure that the
frame is rectangular.
**Parallelogram then Rectangle