Question

Please help me with questions 1-4, I really want to pass this class and I don't understand

Answer 1

1. a=3, b=1
2. x=30, y=50
3. x=18, y=9
4. x=2, y=4.5

Explanation:

You want to find the values of the variables in various expressions for angles, sides, or diagonals of parallelograms.

Parallelograms

A parallelogram is a quadrilateral (4-sided polygon) with opposite sides parallel. The opposite sides are also the same length.

Opposite angles in a parallelogram are congruent (have the same measure), and adjacent angles are supplementary (total 180°).

The diagonals of a parallelogram bisect each other, so the halves of a diagonal are the same length.

These are the relationships you need to know in order to solve these problems.

1.

Opposite sides are the same length.

XY = WZ

3a -4 = a +2

2a = 6 . . . . . . . . . add 4-a to both sides

a = 3

and ...

YZ = XW

2b = b +1

b = 1 . . . . . . . . . subtract b

2.

Opposite angles are congruent.

∠C = ∠A

2y -40 = y +10

y = 50 . . . . . . . . . . add 40-y to both sides

Adjacent angles are supplementary

(y+10) +4x = 180

50 +10 +4x = 180 . . . use the above value for y

4x = 120 . . . . . . . . . . subtract 60

x = 30 . . . . . . . . . . . divide by 4

3.

Diagonals bisect each other. Call the center point X where the diagonals cross.

HX = PX

x -3 = 15

x = 18 . . . . . . . add 3

and ...

EX = QX

y +3 = 12

y = 9 . . . . . . . subtract 3

4.

Same as problem 3.

NX = LX

4x = x +6

3x = 6 . . . . . . . subtract x

x = 2 . . . . . . . divide by 3

and ...

MX = OX

5y -8 = 3y +1

2y = 9 . . . . . . . . add 8-3y to both sides

y = 4.5 . . . . . . . divide by 2

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Additional comment

In general, geometry problems of this sort are solved by making use of the relationships between angles, sides, perimeter, and area of geometric figures. You are expected to remember facts and formulas about these figures that would help you write equations and solve problems like this.

A rhombus is a special parallelogram that has perpendicular diagonals. A rectangle is a special parallelogram that has right-angle corners and congruent diagonals. A square is a special of both of those: a rectangle with perpendicular and congruent diagonals.