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Learn about midpoints of sides, slopes, parallelograms, and quadrilaterals. Discover how to verify geometric figures through diagrams and calculations. Explore properties like parallel sides and equal lengths.
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Properties of Triangles and Quadrilaterals …what you should have learned…
Investigation #1: Midpoints of Triangle Sides - Length • ‘x’ is half the length of ‘y’ y x • ‘y’ is twice the length of ‘x’ • If ‘x’ is 6 cm long, ‘y’ is….. 12 cm • If ‘y’ is 32 m long, ‘x’ is….. 16 cm
y x Investigation #2: Midpoints of Triangle Sides - Slopes the lines are parallel
Diagonals of Parallelograms • the diagonals of parallelograms intersect at their midpoints.
Midpoints of Quadrilateral Sides • when the midpoints of any quadrilateral are connected, the interior figure is always a parallelogram.
Verifying Properties of Geometric Figures What does it mean to ‘verify’? Prove Give evidence
To verify… • Draw a labeled diagram • Decide what properties you will need to show are true • Complete calculations • Make ‘therefore statements’ to conclude that the conditions for the specified figure are met.
#1 – parallelogram • Opposite sides are parallel • Opposite sides are equal in length
#2 – right triangle • Two sides are perpendicular (have negative reciprocal slopes)
#3 – rhombus • Opposite sides are parallel • All sides are equal in length
#4 – rectangle • Adjacent sides are perpendicular • Opposite side are equal in length
