Question

what are properties of the parallelogram ?​

Answer 1

Answer:

6 Properties of Parallelograms Defined

1. Opposite sides are parallel

Segment AB is parallel to segment DC, and segment AD is parallel to segment BC.

2. Opposite sides are congruent

Segment AB is congruent to segment DC, and segment AD is congruent to segment BC.

3. Opposite angles are congruent

Angle A is congruent to angle C, and angle D is congruent to angle B.

4. Same-Side interior angles (consecutive angles) are supplementary

Angles A and D are supplementary, angles B and C are supplementary, angles A and B are supplementary, and angles D and C are supplementary.

5. Each diagonal of a parallelogram separates it into two congruent triangles

Triangle DAB is congruent to triangle DCB.

6. The diagonals of a parallelogram bisect each other

Segment AE is congruent to segment CE, and segment DE is congruent to segment BE.

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Answer 2

Step-by-step explanation:

$\huge \purple{ \sf \: annyeong}$

$\boxed{ \bf \: There \: are \: six \: important \: properties \: of \: parallelograms  \: }$

• Opposite sides are congruent (AB = DC).
• Opposite angels are congruent (D = B).
• Consecutive angles are supplementary (A + D = 180°).
• If one angle is right, then all angles are right.
• The diagonals of a parallelogram bisect each other.
• Each diagonal of a parallelogram separates it into two congruent triangles.

$\begin{gathered} \\ \rule{200pt}{3pt} \end{gathered}$

Example

Q. Prove that when the diagonals of a parallelogram bisect each other at 90∘, it is a rhombus.

Ans. let us prove that ΔAEB and ΔAED are congruent.

AE = AE

BE = ED

∠AEB = ∠AED = 90∘

Therefore, by SAS Congruency, ΔAEB and ΔAED are congruent.

⇒AB = AD

Similarly,

considering congruent triangles ΔAED and ΔCED

⇒AD = DC

This shows that:

AB = BC = CD = AD, which proves that this parallelogram is a rhombus.

Therefore, the given parallelogram is a rhombus.