squares, rhombi and trapezoids:
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Squares, Rhombi and Trapezoids:. Squares, Rhombi and Trapezoids:. Rhombus:. Squares, Rhombi and Trapezoids:. Rhombus: A parallelogram with four congruent sides. Squares, Rhombi and Trapezoids:. Rhombus: A parallelogram with four congruent sides. Squares, Rhombi and Trapezoids:. - PowerPoint PPT PresentationTRANSCRIPT
Squares, Rhombi and Trapezoids:
Squares, Rhombi and Trapezoids:
• Rhombus:
Squares, Rhombi and Trapezoids:
• Rhombus:– A parallelogram with four congruent sides.
Squares, Rhombi and Trapezoids:
• Rhombus:– A parallelogram with four congruent sides.
Squares, Rhombi and Trapezoids:
• In addition to all the properties of a parallelogram, a rhombus has three additional properties:
Property Picture
1. Opposite sides parallel.
2. Opposite sides congruent
3. Opposite angles congruent.
4. Consecutive angles supplementary.
5. Diagonals bisect each other.
6. Four congruent sides.
7. Diagonals are perpendicular.
8. Diagonals bisect opposite angles.
RSTV is a rhombus.
• If the measure of angle SWT = (2x+8) find X.
S T
R V
W
RSTV is a rhombus.
• If the measure of angle SWT = (2x+8) find X.
• What do you know?
S T
R V
W
RSTV is a rhombus.
• If the measure of angle SWT = (2x+8) find X.
• What do you know? SWT is a right angle.
S T
R V
W
RSTV is a rhombus.
• If the measure of angle WRV = (5x+5) and WRS = (7X -19). What is the value of X?
S T
R V
W
RSTV is a rhombus.
• If the measure of angle WRV = (5x+5) and WRS = (7X -19). What is the value of X?
What do you know?
S T
R V
W
RSTV is a rhombus.
• If the measure of angle WRV = (5x+5) and WRS = (7X -19). What is the value of X?
What do you know? The angles are equal.
S T
R V
W
In rhombus DLMP, DM=24, angle LDO=43, and DL=13. Find each of the
following:• OM =• Angle DOL=• Angle DLO=• Angle DML=• DP=
D L
P M
O
Squares:
Squares:
• A parallelogram with four congruent sides and four right angles.
Squares:
• A parallelogram with four congruent sides and four right angles.
• Since a square is a special parallelogram, it has all the properties of a parallelogram, in addition to those of a rectangle and a rhombus.
Squares:Property Picture1. Opposite sides parallel.
Opposite sides congruent.
Opposite angles congruent.
Consecutive angles supplementary.
Diagonals bisect each other.
Four right angles.
Diagonals congruent.
Four congruent sides.
Diagonals are perpendicular.
Diagonals bisect opposite angles.
MATH is a square.
AM
TH
If MA=8, then AT=Angle HST=Angle MAT=If HS=2, then HA= and MT=
S
MATH is a square.
AM
TH
If angle AED=(5X+5) find xX=
S
MATH is a square.
AM
TH
If angle AED=(5X+5) find xX=
If angle BAC=(5X) find xX= S
Write down the key for trapezoids and put in a sketch of each.
Term Definition Sketch
Trapezoid A quadrilateral with exactly one pair of parallel lines
Bases The parallel sides.
Legs The non-parallel sides.
Base Angles Angles at the bases.
Median A segment that joins the midpoints of the legs of a trapezoid. It is parallel to the bases.
Median:
• You can find the length of the median by averaging the two bases.
In trapezoid ABCD, EF is a median. Find each of the following:
AB=25, DC=13, EF=
AE=11, FB=8, AD= BC=
AB=29, EF=24, DC=
AB=7Y+6, EF=5Y-3, DC=Y-2, Y=
D
E
A
F
B
C
Isosceles Trapezoid:
• A trapezoid with congruent legs.
Isosceles Trapezoid:
• A trapezoid with congruent legs.
Isosceles Trapezoid:
• A trapezoid with congruent legs.– Exactly one pair of parallel sides.– Median is the average of the bases.– Legs are congruent.– Diagonals are congruent.– Base angles are congruent.
DONE is an isosceles trapezoid. Angle EDO=110 and angle DEN = (15X-5). Find X.
D
S
E N
O
DONE is an isosceles trapezoid. EO=3X-7 and DN=20. Find X.
D
S
E N
O
