4. Find x and y so that the quadrilateral is a parallelogram.(3y+5)0

(5y­13)0

4x­17

2x­1

Draw a labeled diagram. Show all work.

5. In parallelogram ABCD, m≮A = (2x + 50)o and m≮C = (3x + 40)o. Find m≮B.

6. In parallelogram ABCD, m≮A = (2x -10)o and m≮B = (5x + 15)o. Find m≮C.

7. In parallelogram ABCD, diagonals AC and BD intersect at E. If BE = 4x - 12 and DE = 2x + 8, find x and BD.

8a) Find the value of x and y that will make ABCD a parallelogram.

b) Then find the measure of each angle of the parallelogram.

m≮B = (2y - 3x)o m≮C = (x + y)o m≮D = (5x - y)o

28

                                                  

fAim #29: How do we prove a parallelogram is a rectangle?

3) In rectangle ABCD, AE = 3x + y, EC = 2x + y + 7 and DE = 2y + 3x - 1. Find the values of x and y.

CC Geometry H

Do Now: 1) A rectangle is a parallelogram: Always/Sometimes/Never

2) Which is not true about a rectangle?a) Diagonals bisect each other.b) Opposite angles are congruent.c) Diagonals bisect the angles.d) Diagonals are congruent.

A B

CD

E

Proving a property of a rectangle:If a parallelogram is a rectangle, then its diagonals are congruent.

G H

IJ

Given: Rectangle GHIJProve: GI ≅ HJ

Statements Reasons

Given: Rect. RSTU, M is midpoint of RSProve: ΔUMT is isosceles

Statements Reasons

1a) In ABCD, AE = 7x - 1, and EC = 5x + 5. Find AC.

b) If DB = 10x + 10, find DB.

c) What kind of parallelogram is ABCD and justify your response.

B C

D

E

A

2) The length of a rectangle is seven more than the width. A diagonal is one more than twice the width. Find the width, length and the length of the diagonal using an algebraic solution.

To prove a parallelogram is a rectangle, prove one of the following:

1. ________________________________________________

2. _______________________________________________

***An equiangular quadrilateral is a rectangle.***3.

Statements Reasons

Given:

Prove: ECBF is a rectangle

C B

ADE F

Given: Rect. ABCDProve: ≮CAD ≅ ≮BDA

Statements Reasons

Given: Rect. PQRS Prove: ≮1 ≅ ≮2

Q R

SP

1

2

M

Statements Reasons

A

B C

D

E

Name _________________ Date ____________

1) Rectangle ABCD is shown below. Find x:

A

B C

D

20

4x ­ 2y 3x + yE

2) The length of two adjacent sides of a rectangle differ by 17. If the perimeter of the rectangle is 146, compute a diagonal and the area of the rectangle. Solve algebraically.

3) Given: Rect. ABCD,Prove: a) ΔABP ≅ ΔDCN

b)

A B

CD

N

P

E

Statements Reasons

CC Geometry H HW #29

Mixed review:1) Construct the following using a compass and straightedge:

a. Median from vertex A b. Altitude from vertex A.

A A

4) In rectangle ABCD shown below, AC and BD are diagonals. If m≮1 = 49, find m≮ADB.

A

B C

D1

For #s 5 and 6, refer to rectangle ABCD shown below, with diagonals AC and BD intersecting at R.

A

B C

D

R

5) If DR = 4(3x - 10) and CR = 3(x - 2) + 12, find x, AR, AC, and BD.

6) If AC = 3(2x + 5) - (4x + 4) and BD = (12x - 3) + 5x, find x, AC, and DR.