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Test, state and prove a theorem that defines a set of minimum congruence criteria for each...

Test, state and prove a theorem that defines a set of minimum congruence criteria for each of the following quadrilaterals: parallelograms, rectangles, and rhombi.

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Expert Solution

1. Definition: a four-sided plane rectilinear figure with opposite sides parallel.

Properties of a parallelogram :

  • Opposite sides are parallel and congruent.
  • Opposite angles are congruent.
  • Adjacent angles are supplementary.
  • Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles.

Prove : If a quadrilateral is a parallelogram, it has two pairs of opposite sides congruent.

Given : Parallelogram ABCD

Prove :   

                                                        

Proof :

2. Definition : A rectangle is a parallelogram with four right angles.

Properties of a rectangle :

  • Opposite sides are parallel and congruent.
  • All angles are right.
  • The diagonals are congruent and bisect each other (divide each other equally).
  • Opposite angles formed at the point where diagonals meet are congruent.
  • A rectangle is a special type of parallelogram whose angles are right.

Prove: If a parallelogram is a rectangle, it has congruent diagonals.

Given : Rectangle ABCD

Prove:

Proof:

3. Definition : A rhombus is a parallelogram with four congruent sides.

Properties of a Rhombus :

  • All sides are congruent.
  • Opposite angles are congruent.
  • The diagonals are perpendicular to and bisect each other.
  • Adjacent angles are supplementary
  • A rhombus is a parallelogram whose diagonals are perpendicular to each other.

Prove : If a parallelogram is a rhombus, it has diagonals bisecting the angles

Given : Rhombus ABCD

To Prove :

                

Proof :

*Dear student, I hope the above things will interest you. Please provide a feedback*

milcah answered 2 years ago
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