…what you should have learned…. Investigation #1: Midpoints of Triangle Sides - Length x y ‘x’ is half the length of ‘y’ ‘y’ is twice the length of ‘x’

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Presentation transcript:

…what you should have learned…

Investigation #1: Midpoints of Triangle Sides - Length x y ‘x’ is half the length of ‘y’ ‘y’ is twice the length of ‘x’ If ‘x’ is 6 cm long, ‘y’ is….. If ‘y’ is 32 m long, ‘x’ is….. 12 cm 16 cm

Investigation #2: Midpoints of Triangle Sides - Slopes x y  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 Prove Give evidence What does it mean to ‘verify’?

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