Question

what is midpoint theorem ?​

Answer 1

QUESTION→

What is midpoint theorem?

ANSWER→

Mid point theorem :-

A mid-point of a line segment divides the line segment into two equal parts .

Let a line segment AB in which O is the midpoint..

A_________________O________________B

Now let the co-ordinate of the points as

A→(x¹,y¹)

B→(x²,y²)

C→(x , y)

Formula to find the co-ordinate of that mid-point...... ↓

Co-ordinate of the point be (x,y)

For 'X'=== X¹+x²/2

For 'y'===y¹+y²/2

Note:-

••2 is divided by whole x¹+x²... not only with x²

••2 is divided by whole y¹+y².....not only with y²

By using this Formula uh can find co-ordinate of mid point dividing the line segment into two equal parts

Answer 2

hello ,friend ,i will explain in brief;

Mid-Point Theorem :-

 The line segment joining the mid-points of two sides of a triangle is parallel to the third side and equal to half the third side.Given: In triangle ABC, P and Q are mid-points of AB and AC respectively.To Prove: i) PQ || BC ii) PQ = 1/ 2 BCConstruction: Draw CR || BA to meet PQ produced at R.Proof:

 ∠QAP = ∠QCR. (Pair of alternate angles)

---------- (1)AQ = QC. (∵ Q is the mid-point of side AC)

---------- (2)∠AQP = ∠CQR (Vertically opposite angles)

---------- (3)Thus, ΔAPQ ≅ ΔCRQ (ASA Congruence rule)PQ = QR. (by CPCT). or PQ = 1/ 2 PR

---------- (4)⇒ AP = CR (by CPCT)

........(5)But, AP = BP.

(∵ P is the mid-point of the side AB)⇒ BP = CRAlso.

BP || CR.

(by construction)In quadrilateral BCRP, BP = CR and BP || CR

Therefore, quadrilateral BCRP is a parallelogram.

BC || PR or, BC || PQAlso, PR = BC (∵ BCRP is a parallelogram)⇒ 1 /2 PR = 1/ 2 BC⇒ PQ = 1/ 2 BC.

[from (4)]You

..Thank you!!