Lesson 9 Guess My Parallelogram Practice Understanding

Learning Focus

Classify and justify types of parallelograms based on characteristics of their angles and diagonals.

Can I classify parallelograms as squares, rectangles, or rhombuses based on a few given characteristics or properties, such as characteristics about consecutive angles or characteristics about their diagonals?

Open Up the Math: Launch, Explore, Discuss

Kia and Kamalani are playing a guessing game in which one person describes some of the features of a parallelogram they have drawn and the other person has to name the type of parallelogram: square, rectangle, or rhombus.

Here are some of the clues they gave each other. Decide what type of parallelogram they are describing and explain how you know.

1.

The diagonals of this parallelogram are perpendicular to each other.

2.

Consecutive angles of this parallelogram are supplementary (that is, they add to $180 °$ ).

3.

The diagonals of this parallelogram are congruent.

4.

When rotated $90 °$ , each diagonal of this parallelogram gets superimposed on top of the other.

5.

Consecutive angles of this parallelogram are congruent.

Ready for More?

Here is one more puzzle:

The diagonals of this parallelogram are congruent and perpendicular to each other.

Write a proof to justify your conclusion.

Takeaways

Today, we proved the following theorems about the properties of the diagonals of different types of parallelograms:

We also proved the following theorem about parallelograms in general:

Based on today’s lesson, I have some additional strategies for thinking about the proof:

Lesson Summary

In this lesson, we expanded our ways of thinking about proofs by starting with statements where we first had to decide what we were given and what we were trying to prove. We had to create our own diagrams and mark congruent parts as they became apparent to us based on reasoning with a diagram. We noticed that carefully sequencing proofs allows us to draw upon some theorems to prove other, more complicated theorems.

Retrieval

1.

The diagram is a scale drawing of the layout of a storage room. The numbers on the diagram need to be multiplied by $6$ to get the corresponding measurements in feet for the actual room. Find the perimeter of the real-life size room.

2.

Draw a sketch of a parallelogram. Then prove that the opposite sides of a parallelogram are congruent.