Download Section 5.5 Properties of Parallelograms ANS

Section 5.5 Notes: Properties of Parallelograms
Goals of the lesson:
• Discover properties of parallelograms
• Learn new vocabulary related to vectors
• Continue to develop inductive reasoning and cooperative behavior
Homework: Complete pg. 283-286 # 1-6, 13, 15-17, 19
Ideas covered in this section: Parallelogram Opposite Angles Conjecture, Parallelogram Consecutive Angles
Conjecture, Parallelogram Opposite Sides Conjecture, Parallelogram Diagonals Conjecture
Warm up:
1. Find the length of the midsegment in the trapezoid below.
2. In the triangle below, M, N and P are the midpoints of the sides. Name a segment parallel to the one
given.
3. Find EF.
A parallelogram is a quadrilateral whose opposite sides are parallel. In this activity, you will investigate
properties of parallelograms. If you need help, please ask one of your group mates.
Investigation: Four Parallelogram Properties
Sketch:
First, you will construct a parallelogram using the definition.
Step 1: Construct segment AB and point C above the segment.
Step 2: Construct a line through C parallel to segment AB. (Select the segment and the point and choose
Construct | Parallel Line.)
Step 3: Construct segment AC.
Step 4: Construct a line through B parallel to segment AC.
Step 5: Construct the point of intersection of the two lines. Label the point D.
Step 6: Hide both lines, and finish your parallelogram by constructing the missing segments.
Step 7: Drag different vertices of your parallelogram to check that you constructed it properly.
Step 8: Measure all four angles of your parallelogram.
Investigate:
1. Drag the vertices to observe these angle measures, then fill in the blank below of the Parallelogram
Opposite Angles Conjecture. Write the complete conjecture in your sketch and in your notes.
Parallelogram Opposite Angles Conjecture: The opposite angles of a parallelogram are ______________.
2.
Choose Number | Calculate to add the measures of ALL of the pairs of consecutive angles in your
parallelogram. Note: There should be four consecutive pairs. Drag vertices to observe these angle
sums, then fill in the blank below for the Parallelogram Consecutive Angles Conjecture. Write the
complete conjecture in your sketch and in your notes.
Parallelogram Consecutive Angles Conjecture: The consecutive angles of a parallelogram are
_______________________________.
3. Measure the lengths of ALL four sides of your parallelogram. Drag the vertices to observe these
lengths, then fill in the blank for the Parallelogram Opposite Sides Conjecture. Write the complete
conjecture in your sketch and in your notes.
Parallelogram Opposite Sides Conjecture: The opposite sides of a parallelogram are ________________.
4.
Construct the diagonals of your parallelogram and their point of intersection. Label this point E.
Measure AE, ED, CE, EB. Drag the vertices to observe these lengths, then fill in the blank for the
Parallelogram Diagonals Conjecture. Write the complete conjecture in your sketch and in your notes.
Parallelogram Diagonals Conjecture: The diagonals of a parallelogram ___________________ each other.
Submit:
When you are finished, name the Sketch (with everything completed and measured and all of the conjectures
typed in the sketch), Properties of Parallelograms and submit it to drop box which can be found on Haiku
Chapter 5 Sketch Pad Activities page Section 5.5.
Summarize all of the properties of parallelograms in the space below:
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•
•
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Opposite angles are congruent
Consecutive angles are supplementary
Opposite sides are congruent
Diagonals bisect each other (which means they meet at the same midpoint)
Example 1: ABCD is a parallelogram.
Try on your own: Complete the following problems using the properties that you just learned.
In Exercises 1 – 6, ABCD is a parallelogram.
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തതതത
തതതത and ‫ܨܦ‬
തതതത ∥ ‫ܤܣ‬
7. Given that ‫ܩܣ‬