Geometry

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Geometry

• 5.4 Special Parallelograms

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Set Up a Flow Chart to Fill in as We Go
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Rectangle

• A quadrilateral with four right angles.

Why is a rectangle a parallelogram?
Both Pairs of Opp. Angles are Congruent
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Rhombus

• A quadrilateral with four congruent sides.

Why is a rhombus a parallelogram?
Both Pairs of Opp. Sides are Congruent
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Square (Rhom-tangle Ha! Ha!)

• A quadrilateral with four congruent sides and
  four right angles.

Why is a rhombus a parallelogram?
Both Pairs of Opp. Sides are Congruent
Both Pairs of Opp. Angles are Congruent
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Review Rectangles, Rhombuses, and Squares all
Share these Properties of a Parallelogram

• Opp. Sides are //
• Opp. Angles are congruent
• Opp. Sides are congruent
• Diagonals Bisect Each Other
• In addition, rectangles, rhombuses, and squares
  all have their own special properties. These are
  the focus of this lesson.

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Theorem The diagonals of a Rectangle are
Congruent

• Draw two congruent intersecting lines that bisect
  each other.
• Connect the corners. You drew a rectangle.

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Theorem The diagonals of a rhombus are
perpendicular.

• Draw two lines that bisect each other are
  perpendicular.
• Connect the corners. You have drawn a rhombus.

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Theorem Each diagonal of a rhombus bisects two
angles of the rhombus.

• Draw a rhombus and its diagonals.
• You bisected all four angles.

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Theorem The midpoint of the hypotenuse of a
right triangle is equidistant from all three
vertices.

• Draw a right triangle and put a point at the
  midpoint of the hypotenuse.
• Draw a line from that point to the vertex of the
  right angle.
• All three distances are equal.

.
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Theorem If an angle of a parallelogram is a
right angle, then the parallelogram is a
rectangle.

• Draw one right angle.
• Draw the two other sides parallel to the opposite
  side.
• You have drawn a rectangle.

Why is it a rectangle?
Opp. Angles of a Parallelogram Are congruent
Parallel lines imply SS Int. angles are
supplementary.
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Theorem If two consecutive sides of a
parallelogram are congruent, then the
parallelogram is a rhombus.

• Draw two congruent sides of an angle.
• Draw the two other sides parallel
• to the opposite sides.
• You have drawn a rhombus.

Why is it a rhombus?
Opp. Sides of a Parallelogram are congruent.
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Given Quad. WXYZ is a rectangle. Complete the
statements with numbers. Make sure your and
are clear!
3. If TX 4.5, then WY _____. 4. If WY 3a
16 and ZX 5a 18, then a _____, WY _____
and ZX _____. 5. If mltTWZ 70, then mltTZW
_____ and mltWTZ _____.
X
W
T
Z
Y
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Given Quad. ABCD is a rhombus. Complete the
statements with numbers.
7. If mlt4 25, then mlt5 _____. 8. If mltDAB
130, then mltADC _____. 9. If mlt4 3x 2 and
mlt5 2x 7, then x ____, mlt4 ____, and mlt5
____. 11. If mlt2 3y 9 and mlt4 2y 4,
then y _____, mlt2 _____, and mlt4 ____.
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Given Quad. JKLM is a square. Complete the
statements with numbers.
L
M
x
14. If JL 18, then MK _____, JX _____, and
XK _____. 15. mltMJK _____, mltMXJ _____
and mltKLJ _____.
X
K
J
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HW

• P. 186 (1-11)
• P. 187 (1-10) (11-27 Odd)
• If you forget the theorems, it helps to draw a
  picturei.e. draw a rhombus and then its
  diagonals and see if they are congruent or
  pependicular.

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A HW Jumpstart P. 187 5-8
Property Parallelogram Rectangle Rhombus Square




5) Diags. Bisect each other
X
X
X
X
6) Diags. Are conguent
X
X
7) Diags. Are Perpendicular
X
X
8) A diagonal Bisects 2 angles
X
X