Question

explain mid point theoram​

Answer 1

Step-by-step explanation:

Construction- Extend the line segment DE and produce it to F such that, EF=DE.

In the triangle, ADE, and also the triangle CFE

EC= AE —– (given)

∠CEF = ∠AED {vertically opposite angles}

EF = DE { by construction}

hence,

△ CFE ≅ △ ADE {by SAS}

Therefore,

∠CFE = ∠ADE {by c.p.c.t.}

∠FCE= ∠DAE {by c.p.c.t.}

and CF = AD {by c.p.c.t.}

The angles, ∠CFE and ∠ADE are the alternate interior angles. Assume CF and AB as two lines which are intersected by the transversal DF.

In a similar way, ∠FCE and ∠DAE are the alternate interior angles. Assume CF and AB are the two lines which are intersected by the transversal AC.

Therefore, \(CF \parallel AB\)

So, \(CF \parallel BD\)

and CF = BD {since BD = AD, it is proved that CF = AD}

Thus, BDFC forms a parallelogram.

By the use of properties of a parallelogram, we can write

\(BC \parallel DF\)

and BC = DF

\(BC \parallel DE\)

and DE = (1/2 * BC). Hence Proved.

The Mid- Point Theorem can also be proved by the use of triangles. The line segment which is on the angle, suppose two lines are drawn in parallel to the x and the y-axis which begin at endpoints and also the midpoint, then the result is said to be two similar triangles. This relation of these triangles forms the Mid- Point Theorem.

Answer 2

Answer:

Mid point theorem states that the line joining mid point of two opposite side

of a triangle is parellel as well as half

3rd side or base side.