Properties of Parallelograms

Intro to Parallelograms

Sides and Angles of Parallelograms

A quadrilateral with parallel opposite sides is called a parallelogram.

Math Focus 1: Definition of Parallelograms

Activity 1: Check Your Guess 1

Recall your prior knowledge on quadrilaterals, parallelograms, rectangles, squares, rhombi, trapezoids and kites. In the quiz that follows, choose True if you guess on the statement is true; otherwise, choose False.

Multiple Choice

A quadrilateral is a parallelogram if both pairs of opposite sides are parallel.

• True

• False

Multiple Choice

A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

• True

• False

Multiple Choice

A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

• True

• False

Multiple Choice

A quadrilateral is a parallelogram if any two consecutive angles are complementary.

• True

• False

Multiple Choice

A quadrilateral is a parallelogram if exactly one pair of adjacent sides is perpendicular.

• True

• False

Multiple Choice

A quadrilateral is a parallelogram if one pair of opposite sides are both congruent and parallel.

• True

• False

Math Focus 2: Conditions Which Guarantee that a Quadrilateral is a Parallelogram

• Both pairs of opposite sides are parallel. 

• Both pairs of opposite sides are congruent. 

• Both pairs of opposite angles are congruent

• Diagonals bisect each other.

• If each diagonal divides the quadrilateral into two congruent triangles.   

• A pair of opposite sides are congruent and parallel. 

Using the conditions specified in Math Focus 2

Activity 2: Parallelogram or Not

Identify if the given figure is a parallelogram. If it is a parallelogram, state the condition from Math Focus 2 that supports your answer.

Open Ended

1. Identify if the given figure is a parallelogram. If it is a parallelogram, state the condition from Math Focus 2 that supports your answer.

Open Ended

2. Identify if the given figure is a parallelogram. If it is a parallelogram, state the condition from Math Focus 2 that supports your answer.

Open Ended

3. Identify if the given figure is a parallelogram. If it is a parallelogram, state the condition from Math Focus 2 that supports your answer.

Open Ended

4. Identify if the given figure is a parallelogram. If it is a parallelogram, state the condition from Math Focus 2 that supports your answer.

Math Focus 3: Properties of Parallelograms

Activity 3: Using the Properties of Parallelograms

Supply what is missing in the statement by applying the properties of a parallelogram from Math Focus 3.

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

1. $\overline{MA}\ \cong$

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

2. $\Delta MAH\cong$

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

3. $\overline{MS}\cong$

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

4. $\Delta THM\cong$

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

5. $\angle ATH\cong$

 

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

6. If $m\angle MHT=100$ , then $m\angle MAT=$

 

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

7. If $m\angle AMH=100$ , then $m\angle MHT=$

 

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

8. If  $MH\ =7$ , then $AT=$

 

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

9. If $AS\ =\ 3$ , then $AH=$

 

Fill in the Blanks

Refer to the given figure at the right and answer the following. MATH is a parallelogram.

10. If $MT\ =\ 9$ , then $SM\ =$