RECTANGLES
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RECTANGLES • Recognize and apply properties of rectangles. • Determine whether parallelograms are rectangles. Parts of the tennis court are marked by parallel and perpendicu lar lines.
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RECTANGLES. Recognize and apply properties of rectangles. Determine whether parallelograms are rectangles. Parts of the tennis court are marked by parallel and perpendicular lines. PROPERTIES OF RECTANGLES. A rectangle is a quadrilateral with four right angles. - PowerPoint PPT Presentation
Transcript of RECTANGLES
RECTANGLES• Recognize and apply properties of rectangles.• Determine whether parallelograms are
rectangles.
Parts of the tennis court are marked by parallel and perpendicular lines.
PROPERTIES OF RECTANGLESA rectangle is a quadrilateral with four right angles.
Since both pairs of opposite angles are congruent, it follows that a rectangle is a special type of parallelogram.
THEOREMDIAGONALS OF A RECTANGLE
If a parallelogram is a rectangle, then the diagonals are congruent.
A B
CD
BDAC
Key Concept RectanglesProperties1. Opposite sides are congruent and
parallel
A B
CD
ADBCDCAB
ADBCDCAB||||
1. Opposite sides are congruent and parallel
2. Opposite angles are congruent
A B
CD
Key Concept RectanglesProperties
DBCA
1. Opposite sides are congruent and parallel
2. Opposite angles are congruent
3. Consecutive angles are supplementary
A B
CD
Key Concept RectanglesProperties
180180180180
AmDmDmCmCmBmBmAm
1. Opposite sides are congruent and parallel
2. Opposite angles are congruent
3. Consecutive angles are supplementary
4. Diagonals are congruent and bisect each other.
A B
CD
Key Concept RectanglesProperties
BDAC
1. Opposite sides are congruent and parallel
2. Opposite angles are congruent
3. Consecutive angles are supplementary
4. Diagonals are congruent and bisect each other.
5. All four angles are right angles.
A B
CD
Key Concept RectanglesProperties
Example 1 Diagonals of a RectangleP O
NM
MNOP is a rectangleMO is 6x + 14, PN is 9x + 5Find x
Example 1 Diagonals of a RectangleP O
NM
MNOP is a rectangleMO is 6x + 14, PN is 9x + 5Find x
Solution:
xxxxx
339
531459146 Diagonals of a rectangle are congruent
Subtract 6x from each side
Subtract 5 from each side
Divide each side by 3
Example 2 Angles of a Rectangle
A D
CB
(4x + 5)°
(9x + 20)°
Find x
Example 2 Angles of a Rectangle
A D
CBSolution:
565139025139020954
xx
xxx Angle addition theorem
Simplify
Subtract 25 from each side
Divide each side by 13
(4x + 5)°
(9x + 20)°
Find x
PROVE THAT PARALLELOGRAMS ARE RECTANGLES
THEOREMIf the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle
A B
CD
BDAC
Example 3 Rectangle on a Coordinate PlaneQuadrilateral F(-4, -1), G(-2, -5), H(4, -2), J(2, 2)Determine whether FGHI is a rectangle.
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1
-1
-2
-3
-4
-5
-4 -2 2 4
F
G
H
J
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