Name_______________________________ 14-10 Quadrilateral Review

Geometry Period ____ Date_______

Quadrilaterals Review

Slope:

m= 𝑦2−𝑦1

𝑥2−𝑥1

Midpoint:

𝑀 = (𝑥1 + 𝑥2

2,𝑦1 + 𝑦2

2)

Distance:

√(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2

1) Line segment AB has endpoints A(2, 8), and B(-2, 2). Line segment CD has endpoints C(6, 3) and D(-6, 7). Do 𝐴𝐵̅̅ ̅̅ and

𝐶𝐷̅̅ ̅̅ bisect each other?

a) What formula will you use to answer this question? ___________________________

b) Do 𝐴𝐵̅̅ ̅̅ and 𝐶𝐷̅̅ ̅̅ bisect each other? Why?

2) Line segment JK has endpoints J(6,5) and K(-1, 4). Line segment UV has endpoints U(2, 3) and V(5, 7). Which

segment is longer (has a greater length)?

a) What formula will you use to answer this question? ________________________

b) Which segment is longer (has a greater length)?

3) Calculate the slopes of AB and CD given that: A(-3,2), B(-2,6), C(2,7)and D(1,3).

Math-Hoo and his friend Hootie did this same problem together after school.

Math-Hoo thinks that AB∥CD, and Hootie thinks that AB≅CD.

True or False: (Explain your selections)

1. Math-Hoo is right. _______________ why? _________________________________

2. They’re both right. _________________ why ? _______________________________

4) Side AB of rectangle ABCD is represented by the equation y = −1

3x + 7. Which equation could represent side BC?

1) y = −1

3x + 4

2) y -3x = + 7

3) y = 2x +4

4) Cannot be determined given an equation

5) In the accompanying diagram of parallelogram ABCD, 𝑚∠𝐷 = 10𝑥 − 10 and 𝑚∠𝐵 = 8𝑥. Find the number of degrees

in m<A.

6) In rectangle LMNO, LM = 5x -11, MN = 2x + 4, NO = 6x – 18. Find the length of LO. DRAW IT!

7) As shown in the diagram of rectangle ABCD below, diagonals and intersect at E.

and

Solve for the length of

8) In the diagram below,

Prove ABCD is a parallelogram

Statements Reasons

1. Given

2. CPCTC

3. CPCTC

4. Alternate Interior Angle Theorem

5. Parallelograms have one pair of opposite congruent and parallel sides

9) The diagonals of a rhombus are 10 and 24. Find the perimeter of the rhombus. WHEN IN DOUBT DRAW IT OUT!

The regents ’s this property!

10) The diagram shows rectangle ABCD, with diagonal . What is the perimeter of rectangle ABCD, to the nearest tenth?

11) An equation of a line perpendicular to the line represented by the equation y = −1

2x-5 and passing through (6,-4) is

12) Prove Quadrilateral ABCD is a rhombus and not a rectangle. A(-3,2), B(-2,6), C(2,7)and D(1,3).

13) Given: Parallelogram ABCD, , and diagonal

Prove:

14) The diagram below shows parallelogram LMNO with diagonal , , and .

Explain why is 40 degrees.

15) In the diagram below, ABCD is a parallelogram, is extended through B to E, and is drawn.

If and , what is ?

1) 44°

2) 56°

3) 68°

4) 112°

16) Line segment NY has endpoints N (-11,5) and Y (5, -7). What is the equation of the perpendicular bisector of NY?

17) Triangle ABC has vertices with , , and . Determine and state a value of x that would make

triangle a right triangle. Justify why is a right triangle. [The use of the set of axes below is optional.]

18) Given shown below, with and , what is an equation of the line that passes through point

and is parallel to ?

(1)

(2)

(3)

(4)

19) In quadrilateral BLUE shown below, .Which information would be sufficient to prove quadrilateral BLUE is a

parallelogram?

1) 3)

2) 4)

The regents ’s this property!

20) What is an equation of a line that is perpendicular to the line whose equation is and passes through

?

1)

3)

2)

4)

21) In parallelogram QRST shown below, diagonal is drawn, U and V are

points on and , respectively, and intersects at W. If ,

, and , what is ?

22) Write the equation of the perpendicular bisector of segment A(4,2) and B(8,6).

23) In square GEOM, the coordinates of G are and the coordinates of O are . Determine and state the

coordinates of vertices E and M. [The use of the set of axes below is optional.]

24) Given: Rhombus ABCD with diagonals DB and AC

Prove: ∡1 ≅ ∡2