Question

9/53

Answer 1

The proof of DE is parallel to BC in the given triangle is shown.

What is defined as the parallel line?

• Parallel lines are defined as two lines that remain the same distance away and never intersect.
• To be parallel, two lines must be driven in the same plane, which is a perfectly flat surface such as a wall or sheet of paper.

As per the given data in the question;

A, B and C are the vertices of a triangle.

• A has coordinates (4, 6)
• B has coordinates (2,-2)
• C has coordinates (-2,-4)

Whereas,

D lies at the midpoint of AB.

E lies at  the midpoint of AC.

The mid piont formula is;

Mid point = (x₁ + x₂ / 2, y₁ + y₂ / 2)

The coordinates of D is found by the mid point formula of coordinates.

Put the coordinates of A (4, 6) and B (2,-2).

D = (4 + 2 / 2, 6 - 2 / 2)

D = (3, 2)

The coordinates of E is found by the mid point formula of coordinates.

Put the coordinates of A (4, 6) and C (-2,-4)

E = (4 - 2 / 2, 6 - 4 / 2)

E = (1, 1)

Now, the slope is calculated by;

m of DE = (y₂ -  y₁)/(x₂ - x₁)

The slope of E is

m of DE = (1 - 2)/(1 - 3) = 1/3

Slope of BC

M of BC = (-4 + 2)/(-4 - 2)

M of BC = 1/2

As, the slope of both line DE and BC are equal. Thus, both line are parallel to each other.

To know more about the parallel line, here

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