Transcript 5.7: Proofs Using Coordinate Geometry

5.7: Proofs Using Coordinate
Geometry
Expectations:
G1.1.5: Given a line segment in terms of its
endpoints in the coordinate plane, determine its
length and midpoint.
G1.4.1 Solve multistep problems and construct
proofs involving angle measure, side length,
diagonal length, perimeter, and area of squares,
rectangles, parallelograms, kites, and trapezoids.
G1.4.2: Solve multistep problems and construct
proofs involving quadrilaterals (e.g., prove that the
diagonals of a rhombus are perpendicular) using
Euclidean methods or coordinate geometry.
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5.7: Coordinate Proofs
In the standard (x,y) coordinate plane, point X has
coordinates (-4,0) and point Y has coordinates (0,-8).
What are the coordinates of the midpoint of XY?
A. (-6, -1)
B. (-2, -4)
C. (0, 2)
D. (2, 4)
E. (6, -1)
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Locating figures on the coordinate
grid for coordinate proofs
- use the origin
- use at least one axis for a side of the polygon.
- if possible try to keep the figure in quadrant i unless it has
reflection symmetry then use quadrants i and ii.
5.7: Coordinate Proofs
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Locate a rectangle on the coordinate grid and label the
coordinates of the vertices. The only numerical
coordinate you may use is 0.
5.7: Coordinate Proofs
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5.7: Coordinate Proofs
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Locate a parallelogram on the coordinate grid and label the
coordinates of its vertices. The only numerical
coordinate you may use is 0.
5.7: Coordinate Proofs
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5.7: Coordinate Proofs
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Locate an isosceles triangle on the coordinate grid and
label the coordinates of its vertices. The only numerical
coordinate you may use is 0.
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5.7: Coordinate Proofs
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Given each set of vertices, determine whether parallelogram
ABCD is a rhombus, a rectangle, or a square. List all that
apply.
,
A(1,5), B(6,5), C(6,10), D(1,10)
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Coordinate Proofs
Prove a triangle midsegment is parallel to and one half the
length of the third side of the triangle.
Remember a midsegment is a segment whose endpoints
are the midpoints of 2 sides of a triangle.
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Assignment
pages 350-352,
numbers 11-27, 32a
5.7: Coordinate Proofs
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