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What can you conclude about the following?Are they congruent or equal?

1.)Pairs of opposite sides

2.)Pairs of opposite angles

3.)Pairs of consecutive

4.)Segments as diagonal


Prove that the following figure is a parallelogram

1.)Opposite sides measurement were both 7 inch and both 9 inch

2.)A parallelogram which has 130 and 50 degree angle


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Sagot :

Answer with Step-by-step explanation:

Congruent and equal are synonymous.

Properties of parallelogram that applies to the Questions 1 - 4, Part 1:

  • Opposite sides are congruent.
  • Opposite angles are congruent.
  • Pairs of consecutive angles are supplementary. The sum of their measures is 180°.  They are equal if and only if the parallelogram is a square or rectangle whose angles are all 90°.
  • Segments of a diagonal are congruent because diagonals of parallelogram bisect each other.  Each diagonal divides the other into two congruent segments.

First Part:

1) Congruent

2) Congruent

3) Not Congruent  

The pairs of consecutive angles are supplementary. Consecutive angles share the same side (included side).

4) Congruent

Second Part:

1.) Opposite sides measurement were both 7 inch, and both 9 inch.

Proof:  Opposite sides of a parallelogram are congruent.

Let's say, in parallelogram ABCD, the opposite sides are:

  • AB and CD;   AB = 7 inches, then CD = 7 inches;  AB ≅ CD
  • AD and BC;   AD = 9 inches, then BC = 9 inches;  AD≅ AD

2.) A parallelogram which has 130° and 50° angles.

Proof:  Consecutive angles of a parallelogram are supplementary.

130° + 50° = 180°  (Supplementary angles total measure is 180°)

See attached image for illustration.

View image Аноним