G.CO.11 WORKSHEET #2 – PATTERSON NAME: _______________________ 1. Determine whether the statement is (A)lways, (S)ometimes, or (N)ever True. 1 a) The diagonals of a rectangle are congruent. b) The diagonals of a parallelogram are perpendicular. c) A parallelogram is a rhombus. d) The diagonals of a rhombus bisect each other. e) A rhombus is equilateral. 2. Quadrilateral ABCD is a parallelogram. a) m∠BAC = 54°, b) m∠ADC = 78°, find m∠DCA = _________ find m∠DAB = _________ A A A A A S S S S S N N N N N c) m∠DCB = 142° & m∠DCA = 37°, find m∠BAC= _________ d) m∠ABC = 73° & m∠DBA = 31°, find m∠DBC = _________ e) AE = 14 cm & DE = 18 cm, find EB = __________ f) EC = 10 cm & EB = 15 cm, find AC = __________ B
A
E
C
D
3. Quadrilateral ABCD is a rhombus. a) m∠ADE = 27°, b) m∠CAB = 71°, find m∠DAE = _________ find m∠CEB = _________ find m∠ABD = _________ d) m∠DAB = 140° c) m∠ABC = 64° find m∠ADE = _________ find m∠ABE= _________ f) AD = 13 cm & BD = 24 cm, B
A
E
C
find AC = __________ e) AE = 3 cm & DE = 4 cm, find DB = __________ find AD = __________ D
4. Quadrilateral ABCD is a rectangle. a) m∠BAC = 27°, b) m∠ADE= 74° find m∠ACB = _________ find m∠DAE= _________ find m∠DAC = _________ find m∠BEC= _________ c) m∠AEB= 144°, find m∠CAB = _________ d) m∠BCA = 78° find m∠DAC = _________ e) DE = 9cm, find AC = __________ f) AD= 6 cm & DC = 8 cm, find AE = __________ E
D
39°
42°
B
E
3x - 3
C
A
D
B
E
C
D
c) Rhombus x = _________ A
A
5. Find the value for the variables. a) Parallelogram b) Parallelogram x = ________ x = _______ d) Rhombus x = ________ A
B
B
E
A
28°
5x - 6
D
34 cm
D
C 3x - 5
C
35°
5x - 15
E
C
B
G.CO.11 WORKSHEET #2 – PATTERSON 2 6. Given parallelogram ABCD, determine the measurements. a) m∠DCB = ___________ b) m∠ADC = ___________ c) m∠ADB = ___________ d) m∠ABD = ___________ e) AD = ___________ f) AB = ___________ A
81°
B
E
D
10 cm
30°
24 cm
C
7. Classify the triangle as specific as you can (by side and by angle). a) In rectangle ABCD b) In rhombus ABCD c) In parallelogram ABCD where m∠DAC = 65°, where m∠EDA = 20°, where m∠DAE = 85° & m∠DBC = 19° what type of Δ is ΔADC? what type of Δ is ΔADC? what type of Δ is ΔDEA? _____________________ _____________________ _____________________ B
A
B
A
A
E
E
D
C
A
B
B
E
C
E
D
C
D
d) In square ABCD, what type of Δ is ΔDAB? ___________________ D
C
8. Determine which quadrilateral has these properties? (Pick all the correct answers). A (Parallelogram) a) Diagonals are congruent _______________________________ b) Equilateral _______________________________ c) Diagonals bisect each other _______________________________ B (Rectangle) C (Rhombus) D (Square) 9. Determine the correct answers. a) A square is a rectangle Always Sometimes b) A parallelogram is a rhombus Always Sometimes c) A rhombus is a square Always Sometimes d) A square is a parallelogram Always Sometimes 10. Given rectangle ABCD and the given information to solve each problem. Never Never Never Never a) AC = 4x – 54 and BD = 33 + 1x, find x = ______ & BD = _______ b) AC = 4x – 60 and AE = x + 5, find x = ______ & EC = ____________ c) m∠BAC = 4x + 12 and m∠DAC = 5x + 24, find x = _____ & m∠DAC = _______ d) AE = 9 cm, DC = 15 cm, find AD = ___________ (2 decimal places) e) m∠EAD = 63°, m∠AED = 4x + 8, find x = ____________ A
B
E
D
C