December 11, 2019

2(a + 3) 5a - 3

68˚

(b - 9)˚

(2c+6)˚10

Warm-upFind the values of the variables in the parallelogram.

a = ___ b = ___ c = ___

3 77 53

December 11, 2019

Geometry 5.4Properties of Rhombuses,

Rectangles and Squares

Learning Target: I can determine the properties of rhombuses,

rectangles and squares and use them to find missing lengths and angles (G-CO.11)

December 11, 2019

defn: quadrilateral w/2 sets of || sides defn: parallelogram w/ 4 rt. ∠s

Properties:1) opp. sides ≅2) opp. ∠s ≅3) consec. ∠s are supp.4) diagonals bisect each other

Properties:1) all properties of2) diagonals are ≅

equiangular

parallelogram

December 11, 2019

defn: parallelogram w/ 4 ≅ sides defn: parallelogram w/ 4 rt. ∠s and 4 ≅ sides

Properties:1) all properties of 2) diagonals are ≅3) diagonals are ⊥4) diagonals bisect ∠s

Properties:1) all properties of2) diagonals are ⊥3) diagonals bisect ∠s

equilateral regularol

so

December 11, 2019

Classify the parallelogram. Explain.

Rhombus SquareRectangle

1. 2.

3. 4.

6.

–– ––

5.

L l rhombus

1 trectangle

square rectangle

0

square rhombus

December 11, 2019

Classify the quadrilateral. Explain.

Iparmainrame

rhombus

II square

December 11, 2019

Classify the special quadrilateral. Then find the values of x and y.

7.

8.m∠NLM = (7y + 3)˚

5 6 8 thy 119718

6 3112g 96

180Z

my84

yab

7yt 3 45

2 1 4 7 74 42

2x 2x9 6

1 2 7

8 2

4 X

December 11, 2019

The diagonals of rectangle PQRS intersect at T. Given that m∠RPS = 62° and QS = 18, find the indicated measures.

9. m∠QPR = ________

10. m∠PTQ = ________

11. ST = ________

12. PR = ________

f180 28 28

28

124 1428 2 L

9 f r18

December 11, 2019

The diagonals of rhombus WXYZ intersect at V. Given the m∠XZY = 34° and WV = 7, find the indicated measures.

13. m∠WZV = ________

14. WY = ________

15. m∠XYZ = ________

16. VY = ________ yZ

V

34 I

14 n

112 it f7 680 112

180 68

December 11, 2019

The diagonals of square EFGH intersect at J. Given that GJ = 15, find the indicated measures.

17. m∠EJF = ________

18. m∠JFG = ________

19. FH = ________

20. EJ = ________

90

45 IsA30

15

December 11, 2019

Assignment: 5.4 worksheet

December 11, 2019

Geo 5.4 wksht answers #1-5

2. Rhombus parallelogram & diag are ⊥

3. Rectangle

Parallelogram & diag ≌

1.

X

X XXXXXXXXX

XXXX

XX XX X

X X

4. Square

Prarallelogram, 4 rt ∠s & 4 ≌ sides 5. Parallelogram

diag bisect each other

December 11, 2019

Geo 5.4 wksht answers #6-126.a. 90˚ b. 56˚ c. 56˚

d. 112˚ e. 5 f. 5

7.a. 53˚ b. 90˚ c. 74˚

d. 37˚ e. 8 f. 16

8.a. 90˚ b. 45˚ c. 45˚

d. 1˚ e. 2

9. FG = 7, x = 30, y = 5 10. x = 6, KM = 30, NL = 30

11. x = 5, WZ = 39 12. x = 13, m∠F = 117˚, m∠E = 63˚