Michael J. answered • 09/05/15

Tutor

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Effective High School STEM Tutor & CUNY Math Peer Leader

Note: I think you meant NP instead of NO. Your finger must have hit the wrong key.

1)

The rhombus will have 4 consecutive sides:

MN, NP, PQ, and MQ

A rhombus has 4 equal sides. So we set the given sides equal to each other.

2a - 3b = 20 - 3b

Since -3b is on both sides of the equation, b can be an infinite number of values as long as b is constant. All that is left is to equate 2a and 20.

2a = 20

a = 10

2)

The sides of the quadrilateral will be arrange as:

AB, BC, CD, and AD

∠A and ∠B are adjacent to each other. ∠C and ∠D are also adjacent to each other. ∠A and ∠C are opposite to each other. These angles are always equal in measure.

You can draw a picture of this to get a better visual.

Parallelograms are 4 sided closed figures that have two pairs of parallel sides that are equal to each other, 2 pairs of equal and opposite angles, and 2 pairs of supplementary angles. If ∠A is an angle less than 90 degrees and ∠B is an angle greater than 90 degrees, these two angles together must form a straight line. These angles are supplement to each other.

3)

A parallelogram is a 4 sided figure with 2 pairs of parallel sides, 2 pairs of equal side lengths, and 2 pairs of opposite and equal angles. A rhombus fits this description.