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
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.