placing figures in the coordinate plane
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Placing Figures in the Coordinate Plane. Lesson 6-6. Review:. Angles of a Kite. You can construct a kite by joining two different isosceles triangles with a common base and then by removing that common base. Two isosceles triangles can form one kite. Angles of a Kite. - PowerPoint PPT PresentationTRANSCRIPT
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Placing Figures in the Coordinate Plane
Lesson 6-6
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Review:
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Angles of a KiteYou can construct a kite by joining two
different isosceles triangles with a common base and then by removing that common base.
Two isosceles triangles can form one kite.Two isosceles triangles can form one kite.
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Angles of a Kite
Just as in an isosceles triangle, the angles between each pair of congruent sides are vertex anglesvertex angles. The other pair of angles are nonvertex anglesnonvertex angles.
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Find the slope….
(a, b)
(3a, b+4)
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Find the midpoint….
(a, b)
(3a, b+4)
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Naming Coordinates
Rectangle KLMN is centered at the origin and the sides are parallel to the axes. Find the missing coordinates.
L(4, 3)
M(?, ?)
K(?, ?)
N(?, ?)
Answer:
K(-4, 3)
M(4, -3)
N(-4, -3)
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Naming Coordinates
Rectangle KLMN is centered at the origin and the sides are parallel to the axes. Find the missing coordinates.
L(a, b)
M(?, ?)
K(?, ?)
N(?, ?)
Answer:
K(-a, b)
M(a, -b)
N(-a, -b)
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Naming Coordinates Use the properties of a parallelogram to find the
missing coordinates. (Don’t use any new variables.
Q(?, ?)
P(s, 0)
K(b, c)
N(0, 0)
Answer:
Q(b + s, c)
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Finding a Midpoint Find the coordinates of the midpoints
T, U, V, and W.
C(2c, 2d)
E(2e, 0)
A(2a, 2b)
O(0, 0)
W
V
U
T
Use midpoint formula:
2,
22121 yyxx
Answer:
T(a, b)
U(e, 0)
V(c + e, d)
W(a + c, b + d)
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Finding a Slope
Find the slope of each side of OACE.
C(2c, 2d)
E(2e, 0)
A(2a, 2b)
O(0, 0)
W
V
U
T
Use slope formula:
12
12
xxyy
Answer:
slope of OA = b / a
slope of AC = d – b / c – a
slope of CE = c – e / d
slope of OE = 0
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Midsegment of a trapezoid
The midsegment of a trapezoid is the segment that connects the midpoints of its legs. Theorem 6.17 is similar to the Midsegment Theorem for triangles.
midsegment
B C
DA
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Theorem 6.17: Midsegment of a trapezoid
The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases.
MN║AD, MN║BC MN = ½ (AD + BC)
NM
A D
CB
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Example
Find the value of x.
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Mmmm cake.
5”
17”2nd layer?
14”
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Assignment
Page 328 #’s 1-11 odd 20 , 23, 28-30, 31 Page 333 #’s 1 , 9