Quadrilateral RSTU, diagonals SU and

RT intersect at point V.

 

RSTU is a parallelogram. If m_TUV = 78° and

m_TVU = 54degrees, explain how you can find the measure of SRV. Show all steps of your work, and refer to any properties of triangles, parallelograms, or triangle congruency theorems as necessary to justify your response

1. The perimeter of a rhombus is 40. What is the area of the square?

2. If one angle of a parallelogram is 60 degrees, find the number of degrees in the remaining three angles.

3. Are the diagonals of a parallelogram perpendicular? Why orwhy not? Explain.

4. Does an isosceles trapezoid have two sets of parallel sides? Why or why not? Explain.

5. Does a rhombus have two sets of congruent sides? Why or why not? Explain.

6. The perimeter of a square is 160 feet. What is the area of the square?

7. True or false;

a. A rhombus is a parallelogram with four congruent sides

b. A rectangle is a parallelogram with four right angles

c. A square is a rectangle and a rhombus

d. A rhombus is always a square

e. Every parallelogram is a regular quadrilateral

f. In a rectangle, the diagonals are perpendicular

8. Name the bases of the trapezoid shown below;

9.True or False;

a. A trapezoid has two bases

b. A trapezoid may have a right angle

c. A trapezoid may have three congruent sides

d. The bases of an isosceles trapezoid are congruent

e. The parallel sides of a trapezoid are called the legs

10. Find the values of the median of a trapezoid with the following base values;

Quadrilateral STUV is :

1. A square

2. A Rectangle

3. A rhombus

4. A parallelogram

5. A generic quadrilateral

Calculate the area of each of the polygons with the following dimensions.

1. Triangles

1. 1. B = 4in, H = 5in
2. 1. B = 6ft, H= 10ft
   2. B = 12m, H = 15m
   3. Application: Sandy is making tablecloths in the shape of triangles. She needs to make two triangle tablecloths for one table. The triangles have base of 2 ft and a height of 4 ft. What is the total area of the triangle tablecloths for one table?

2. Parallelogram (H = height) and (B = base)

1. 1. H = 9in, B = 6in
2. 1. H = 5 ft, B = 2ft
3. 1. H = 7yds, B = 3yds
   2. Application: If a parallelogram has a base of 13 mm and an area of 78 mm2 what is the height?

Hint: Use the formula. Substitute the given values and then solve as an equation.

3. Rectangle (L = length) and (w = width)

1. 1. rect. DKIF with L = 8 ft and w = 6 ft
2. 1. rect. AOPU with L = 13 ft and w = 5 ft
   2. Application: Charles is paining the den. Two walls are 9 ft high and 15 ft long. The other two walls are 8 ft high and 10 ft long. Charles bought one gallon of paint that will cover 440 square feet of wall space. Does he have enough paint? Explain.

4. Rhombus ( d1 = diagonal 1) (d2 = diagonal 2)

1. 1. rhombus with d1 = 12 yds and d2 = 12 yds
2. 1. rhombus with d1 = 10 ft and d2 = 25 ft
3. 1. rhombus with d1 = 16 in and d2 = 22 in
   2. Application: a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?

5. Trapezoid ( b1 = base 1) (b2 = base 2) (H = height)

1. 1. b1 = 6 ft, b2 = 7 ft, H = 10 ft
2. 1. b1 = 5 yds, b2 = 8 yds, H = 4 yds
   2. c. b1 = 9 in, b2 = 11 in, H = 13 in
   3. d. Application: The two bases of a trapezoid = 16 km and its area = 32 km2. What is its height?

Hint: Use the formula. Substitute the given values and then solve as an equation.