Question

Is midpoint theorem and converse of midpoint theorem are same things are not?

Answer 1

Step-by-step explanation:

The mid point theorem states that the line joining the mid points of the sides of a triangle is parallel to the other side.....

whereas,

The converse is just opposite of mid point theorem....it states that if a line is parallel to one side of a triangle and passes through the mid point of the other side of the same triangle then it is said that it will also pass through the mid point of the third side of the same triangle....

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Answer 2

Theorem :

If a line drawn through the midpoint of one side of a triangle and parallel to the other side then it bisects the third side .

For this theorem ' Given ', to prove, ' construction ' is given below. Try to write the proof.

Given :

Point D is the midpoint of side AB of ∆ ABC. Line L passing through the point D and parallel to side BC intersects side AC in point E.

To prove :

AE = EC

Construction :

• Take point F on line L such that D - E - F and DE = EF.
• Draw SEG CF

Proof :

Use the Construction and line L || seg BC which is given. Prove ∆ADE = ∆CFE and complete the proof.

More

Remember this !

• Diagonals of a rectangle are congruent.
• Diagonals of a square are congruent.
• Diagonals of a rhombus are pendicular bisectors of each other.
• Diagonals of a rhombus bisect the pairs of opposite angles.
• diagonals of a square are pendicular bisectors of each other.
• Diagonals of square bisect opposite angles.