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SOLVING PROBLEMS INVOLVING PARALLELOGRAMS,TRAPEZOIDS, AND KITES
Show your solution and write the theorems or properties you applied to justify each step in the solution process. You may illustrate each given, to serve as your guide. Be sure to box your final answer.
1.Given: Quadrilateral WISH is a parallelogram.
a. If m ∠W=x + 15 and m ∠S=2x + 5, what is m ∠W?
b. If WI=3y+3 and HS=y+13, How long is HS(there's a line segment/line segment HS)?
c. (rectangle)WISH is a rectangle and its perimeter is 56 cm. One side is 5cm less than twice the other side. What are its dimensions and how large is its area?
d. What is the perimeter and the area of the largest square that can be formed from rectangle WISH in 1.c.?
2.Given: Quadrilateral POST is an isosceles trapezoid with OS(line segment OS) || PT(line segment PT). ER(line segment ER) is its median:
a.If OS=3x-2, PT=2x+10 and ER=14, how long is each base?
b.If m ∠P=2x+5 and m ∠O=3x-10,what is m ∠T?
c.One base is twice the other and ER is 6cm long. If its perimeter is 27cm, how long is each leg?
d. ER is 8.5 in long and one leg measures 9 in. What is its perimeter if one of the bases is 3 in more than the other?
3.Given: Quadrilateral LIKE is a kite with LI(line segment LI) ≅ IK(line segment IK) and LE (line segment LE) ≅KE (line segment KE.
a.LE is twice LI. If its perimeter is 21 cm, how long is LE(line segment)?
b.What is its area if one of the diagonals is 4 more than the other and IE+LK=16 in?
c. IE=(x-1) ft and LK=(x+2) ft. If its area is 44 ft, how long are IE(line segment IE) and LK(line segment LK)?

Sagot :

Please click image below for the solutions, theorems, properties, definitions as proofs to support the solution.  Illustration also included.



(Note:  Attached files are the edited version of my solution to the same problem posted here: brainly.ph/question/ 279413, especially for question Number 1.)





 
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1. Properties of parallelogram Used: Opposite angles of parallelogram are congruent therefore ∠W = ∠S, so we have to substitute the given value by following the property of parallelogram cited above. 
 ∠W = x + 15
∠S = 2x + 5
Solution:           ∠W = ∠S
Substitute:      x+15 = 2x + 5
                        x-2x = 5-15
                           -x = -10     divide by -1
                             x = 10

                          
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