5.5 Investigation
Four Parallelogram Properties
Step 1: Using the lines on a piece of graph paper as a guide, draw a pair of parallel lines that are at least 6 cm apart. Using the parallel edges of your double-edged straightedge, make a parallelogram. Label your parallelogram LOVE
Step 2: Let's look at the opposite angles. Measure the angles of parallelogram LOVE. Compare a pair of opposite angles using patty paper or your protractor
The opposite angles in parallelogram LOVE are congruent
Parallelogram Opposite Angle Conjecture
The opposite angles of a parallelogram are congruent
Two angles that share a common side in a polygon are consecutive angles. In parallelogram LOVE, angle LOV and angle EVO are a pair of consecutive angles. The consecutive angles of a parallelogram are also related.
Step 3: Find the sum of the measure of each pair of consecutive angles in parallelogram LOVE.
The sum of the measure of each pair of consecutive angles in a parallelogram LOVE are 180 degrees
Share your observation with your group. Copy and complete the conjecture.
Parallelogram Consecutive Angle Conjecture
The consecutive angles of a parallelogram are supplementary
Step 4: Describe how to use the two conjectures you just made to find all the angles of a parallelogram with only one angle measure given.
The two conjectures I just made can be used to find all the angles of a parallelogram with only one angle measure because if I was given a base angle of 70 degrees, I'd know that the opposite angle is congruent to that measurement which would make it also 70 degrees. And I also know that that angle measurement has a consecutive angle which would mean the sum of the two angle would equal 180 and since their supplementary which would make the consecutive angle 110 degrees
Step 5: Next let's look at the opposite sides of a parallelogram. With your compass or patty paper, compare the lengths of the opposite sides of the parallelogram you made.
Share your results with your group. Copy and complete the conjecture.
Parallelogram Opposite Sides Conjecture
The opposite sides of a parallelogram are congruent
Step 6: Finally, let's consider the diagonals of a parallelogram. Construct the diagonals line segment LV and EO, as shown below. Label the point where the two diagonals intersect point M.
Step 7: Measure LM and VM. What can you conclude about point M? Is this conclusion also true for diagonal EO. How to the diagonals relate?
I can conclude that point M is the midpoint of the diagonals from the vertex to the opposite vertex. This conclusion is also true for diagonal EO. The diagonals relate because when intersected, they form two congruent segments
Share your results with your group. Copy and complete the conjecture.
Parallelogram Diagonals Conjecture
The diagonals of a parallelogram are bisectors