Question

write the following sentence in conditional form:
Every rhombus is square​

Answer 1

Step-by-step explanation:

Every rhombus is a square. If the quadrilateral is rhombus, then it is a square. (ii) Angles in a linear pair are supplementary. If angles are in linear pair, then they are supplementary.

Answer 2

Step-by-step explanation:

Expii

GeometryQuadrilaterals: Rhombi

Proving a Quadrilateral 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.

Proving a Quadrilateral Is a Rhombus

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Explanations (1)

Siddharth Namachivayam

Text

3

When proving a quadrilateral is a rhombus, we must know several things:

1) A rhombus is a parallelogram with equal side lengths.

2) A rhombus has diagonals that are perpendicular to one another and bisect one another.

3) A rhombus' diagonals bisect the angles of the vertices each diagonal intersects.

Prove that when in a rectangle, the midpoints of the sides of the rectangle are drawn and labeled

A

,

B

,

C

,

and

D

,

then the quadrilateral

A

B

C

D

is a rhombus.

Say that the rectangle had side lengths of length

e

and

f

.

Then the side lengths of quadrilateral

A

B

C

D

,

by the Pythagorean Theorem, are

√

(

e

2

)

2

+

(

f

2

)

2

.

Since all sides of this quadrilateral are equal then quadrilateral

A

B

C

D

must be a rhombus.