In Exercises 8 to 10, use the properties of rectangles to solve each problem. Rectangle ABCD is shown in the figure.
In Exercise 9 and 10, see the figure for Exercise 8.
Exercises 8 â€“ 10
Given: | AB = x + y and BC = x + 2y, and CD = 2x â€“ y â€“ 1, and DA = 3x â€“ 3y + 1 | |
Find: | x and y |
To find:
x and y of the given rectangle.
The basic property of rectangle:
1) All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other).
2) All angles are right angles by definition.
3) The diagonals are congruent.
Calculation:
Given: AB = x + y and BC = x + 2y, and CD = 2x â€“ y â€“ 1, and DA = 3x â€“ 3y + 1
Consider the rectangle.
Now we have to find x and y of the given rectangle.
To find x and y:
From the property, opposite sides are congruent in rectangle.
So, AB = CD
BC = DA
Now we have to solve (1) and (2).
By solving (1), we get
By solving (2), we get
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