6-3A Tests for Parallelograms

6-3A Tests for Parallelograms

A Quick Review

You may need to use your notes from 1st semester to help you.

Multiple Choice

Q1:  What is this formula used for?

 $\frac{y_2-y_1}{x_2-x_1}$  

• To find the distance between two points

• To find the slope between two points

• To find the midpoint between two points

Multiple Choice

Q2:  What is the formula below used for?

 $\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$  

• To find the distance between two points

• To find the slope between two points

• To find the midpoint between two points

Multiple Choice

Q3: How do you prove two lines are parallel?

• Use the distance formula

• Use the midpoint formula

• Use the slope formula and show the slopes are the same

• Use the slope formula and show the slopes are opposite reciprocals

Time to start your 6-3A Notes

Multiple Choice

Q4: Is the quadrilateral a parallelogram?

• Yes; one pair of opposite sides are parallel

• Yes; one pair of opposite sides are congruent

• Yes; one pair of opposite sides are parallel and congruent

• No; only one pair of sides are parallel

• No; only one pair of sides are congruent

Multiple Choice

Q5: Is the quadrilateral a parallelogram? If yes, pick the statement that explains why.

• Definition of a Parallelogram

• Opposite sides congruent

• Opposite sides parallel and congruent

• Not enough info

Multiple Choice

Q6: Is the quadrilateral a parallelogram? If yes, pick the statement that explains why.

• Opposite sides parallel

• Opposite angles congruent

• Opposite sides congruent and parallel

• Not enough info

Multiple Choice

Q7: Is this quadrilateral a parallelogram?

• Yes. Diagonals bisect each other

• no

• Yes. Opposite angles are congruent

• Yes. Opposite sides are congruent

Multiple Choice

Q8:  Which of the following has the slope formula written correctly?

•  $\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}$

• $\frac{\left(x_2-x_1\right)}{\left(y_2-y_1\right)}$

• $\frac{\left(y_1-y_2\right)}{\left(x_2-x_1\right)}$

• $\frac{\left(x_1-y_1\right)}{\left(x_2-y_2\right)}$

Multiple Choice

Q9: If you can prove that one pair of opposite sides are congruent, you can prove that the shape is a parallelogram.

• True

• False

Multiple Choice

Q10: You can use the slope formula to calculate the lengths of opposite sides of a parallelogram.

• True

• False

Multiple Choice

Q11: What formula would you use to find the length of each side of a parallelogram?

Multiple Choice

Q12: You can prove both pairs of opposite sides are parallel by using the slope formula.

• True

• False

Multiple Choice

Q13: You can prove both pairs of opposite sides are congruent in a parallelogram using the distance formula.

• True

• False

Multiple Choice

Q14:  If I have a parallelogram labeled ABCD and I am going to prove it using the slope formula, what sides need to be parallel?

•  $\ \overline{AB}\ \parallel\ \overline{CD}\ \ and\ \ \overline{AD}\ \parallel\ \overline{BC}$ 

•  $\ \overline{AB}\ \parallel\ \overline{BC}\ \ and\ \ \overline{AD}\ \parallel\ \overline{CD}$ 

•  $\ \ \overline{AD}\ \parallel\ \overline{BC}\ \ and\ \ \overline{AB}\ \parallel\ \overline{BC}$ 

•  $\ \ \overline{AB}\ \parallel\ \overline{AD}\ \ and\ \ \overline{CD}\ \parallel\ \overline{BC}$ 

Multiple Choice

Q15:  If I have a parallelogram labeled ABCD and I am going to prove it using the distance formula, what sides need to be congruent?

•  $\overline{AB}\cong\overline{CD}\ and\ \overline{AD}\cong\overline{BC}$ 

•  $\ \ \overline{AB}\cong\overline{BC}\ and\ \overline{BC}\cong\overline{AB}$ 

•  $\ \ \overline{AB}\cong\overline{CD}\ and\ \overline{CD}\cong\overline{BC}$ 

•  $\ \ \overline{AB}\cong\overline{AD}\ and\ \overline{AB}\cong\overline{AC}$ 

Determine whether the quadrilateral is a parallelogram using 
Opp. Sides  $\cong\rightarrow$  Parallelogram

 $Q\left(-10,\ -2\right),\ R\left(1,\ -1\right),\ S\left(1,\ -7\right),\ T\left(-11,\ -8\right)$  

Be prepared to answer the following questions.

Multiple Choice

Q16:  What is QR?

• $\sqrt{145}$

• $\sqrt{122}$

• $\sqrt{82}$

• $2\sqrt{41}$

Multiple Choice

Q17:  What is ST?

• $\sqrt{145}$

• $\sqrt{122}$

• $\sqrt{82}$

• $2\sqrt{41}$

Multiple Choice

Q18: Is QRST a parallelogram?

• Yes

• No

• Not enough information

Determine whether the quadrilateral is a parallelogram using 
Definition of a Parallelogram

 $K\left(2,\ 7\right),\ L\left(6,\ 12\right),\ M\left(13,\ 13\right),\ N\left(9,\ 8\right)$  

Be prepared to answer the following questions.

Multiple Choice

Q21: Is KLMN a parallelogram?

• Yes

• No

• Not enough information

Determine whether the quadrilateral is a parallelogram using 
One Pair Opp. Sides  $\cong\parallel\rightarrow$  Parallelogram

 $D\left(-5,\ -6\right),\ E\left(5,\ 2\right),\ F\left(4,\ -4\right),\ G\left(-6,\ -12\right)$  

Be prepared to answer the following questions.

Multiple Choice

Q22:  What is DE?

• $4$
  

• $\sqrt{10}$

• $2\sqrt{41}$

• $8\sqrt{20}$

Multiple Choice

Q23:  What is m for $\overline{FG}$   ?

•  $\frac{4}{5}$  

•  $\frac{8}{10}$  

•  $\frac{5}{4}$  

•  $\frac{1}{3}$  

Multiple Choice

Q24: Is DEFG a parallelogram?

• Yes

• No

• Not enough information