Respuesta :

Answer:

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Step-by-step explanation:

The point E intersects the line segment AC and BD at mid-point. And the coordinate of E will be (a + b, c). Then the correct option is B.

What is the midpoint of line segment AB?

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

Let ABCD is a parallelogram.

The coordinates of the parallelogram are given as A(0, 0), B(2b, 2c), C(2a + 2b, 2c), and D(2a, 0).

Let E be the mid-point.

The mid-point of AC will be

[tex]\Rightarrow \left ( \dfrac{2a + 2b}{2},\dfrac{2c}{2} \right )\\[/tex]

⇒ (a + b, c)

The mid-point of BD will be

[tex]\Rightarrow \left ( \dfrac{2a + 2b}{2},\dfrac{2c}{2} \right )\\[/tex]

⇒ (a + b, c)

The point E intersects the line segment AC and BD at mid-point.

Then the coordinate of E will be (a + b, c).

Then the correct option is B.

More about the midpoint of line segment AB link is given below.

https://brainly.com/question/17410964

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