## How do you prove the theorems on rectangle rhombus and square?

THEOREM: If a parallelogram is a rhombus, the diagonals are perpendicular. THEOREM Converse: If a parallelogram has diagonals that are perpendicular, it is a rhombus. A square is a parallelogram with four congruent sides and four right angles.

What are the theorems about square rectangle rhombus?

Rectangle Theorem: A quadrilateral is a rectangle if and only if it has four right (congruent) angles. Rhombus Theorem: A quadrilateral is a rhombus if and only if it has four congruent sides. Square Theorem: A quadrilateral is a square if and only if it has four right angles and four congruent sides.

### How do you prove all the theorems on square?

Prove that : ABCD is a square. 5) Properties of parallelogram. 8) Properties of parallelogram….Square and its Theorems.

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Statements Reasons
4) AB = BA 4) Reflexive (common side)
5) Δ ADB ≅ ΔBCA 5) SAS postulate
6) AC = BD 6) CPCTC
7) OB = OD 7) As square is a parallelogram so diagonals of parallelogram bisect each other.

How do you prove a rectangle is a rhombus?

To prove a quadrilateral is a rhombus, here are three approaches: 1) Show that the shape is a parallelogram with equal length sides; 2) Show that the shape’s diagonals are each others’ perpendicular bisectors; or 3) Show that the shape’s diagonals bisect both pairs of opposite angles.

#### What are the theorems on rectangle?

Rectangle and its Theorems

Statements Reasons
1) ABCD is a rectangle. 1) Given
2) AD = BC 2) Property of rectangle (opposite sides are equal)
3) AB = AB 3) Reflexive (common side)
4) ∠A = ∠B 4) Each right angle.(property of rectangle)

What are the theorems of rhombus?

The opposite sides of a rhombus are parallel.

• The opposite angles of a rhombus are equal.
• The diagonals of a rhombus bisect each vertex angle.
• The diagonals of a rhombus bisect each other at right angles.
• ## How many theorems does rectangle have?

Rectangle and its Theorems

Statements Reasons
2)∴ ABCD is a Parallelogram. 2) Every rectangle is a Parallelogram.
3) AD || BC 3) By Properties of parallelogram.
4) ∠A + ∠B = 1800 4) Interior angles on the same side of transversal are supplementary.
5) 90 + ∠B = 180 5) ∠A = 90 (Given)
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How are rhombus square and rectangle related?

A rectangle has two pairs of opposite sides parallel, and four right angles. It is also a parallelogram, since it has two pairs of parallel sides. A square has two pairs of parallel sides, four right angles, and all four sides are equal. A rhombus is defined as a parallelogram with four equal sides.

### How do you prove a square is a square proof?

How to Prove that a Quadrilateral Is a Square

1. If a quadrilateral has four congruent sides and four right angles, then it’s a square (reverse of the square definition).
2. If two consecutive sides of a rectangle are congruent, then it’s a square (neither the reverse of the definition nor the converse of a property).

How do you verify a rhombus?

If the diagonals of a quadrilateral bisect all the angles, then it’s a rhombus (converse of a property). If the diagonals of a quadrilateral are perpendicular bisectors of each other, then it’s a rhombus (converse of a property).

#### What are the theorems on Rhombus?

What are some important theorems related to the rhombus?

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Then we looked at some of the important theorems related to rhombuses and also saw the proofs for them. Opposite angles in the rhombus are equal. The diagonals of the rhombus bisect each other and are perpendicular to each other.

## What are the definition and theorems of rectangle?

When dealing with a rectangle, the definition and theorems are stated as … A rectangle is a parallelogram with four right angles. If a parallelogram has one right angle it is a rectangle. A parallelogram is a rectangle if and only if its diagonals are congruent.

How do you know if a parallelogram is a rhombus?

If a parallelogram has two consecutive sides congruent, it is a rhombus. A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.

### How do you prove that the diagonals of a rhombus bisect each other?

Thus, the diagonals of a rhombus bisect each other. Now, to prove that the diagonals are perpendicular at the point O, consider the triangles BOC and DOC. In these triangles, we already proved that BO = OD. We know that BC = DC and OC is the common side. Therefore, using the side-side-side property, the triangles BOC and DOC are congruent.