ABC is a triangle. AD is a median of ABC. E is the midpoint of AD and produced to meet AC at F. prove that AF=1/3AC

what is the full form of cpct ?  what does it mean ?

1.if two isosceles triangle have a common base,prove that the line segment joining their vertices bisects the common base at right angles.

2.show that the sum of three medians of a triangle is less than its perimeter.

In a triangle ABC AD is the bisector of angle BAC. Show that AB>BD and AC>CD

 1. If the bisector of an angle of a triangle also bisect the opp. side , prove that the triangle is isos . triangle ?

2. If triangle ABC is right angle at B. such that angle BCA=2 angle BAC . show that hypt.AC =2BC  ?

3. bisector of angle B and angle C of isos. triangle ABC with AB=AC intersect each other at O. Show that external angle adjacent to angle ABC = angle BOC 

4. In a rt. triangle prove that the line segment joining the mid point of the hypt to the opp. vertex is half of the hypt ?

5. line segment joining the midpoint M&N of prallel sides AB and DC . respectivelly of a trap. ABCD is perpendicular to both sides AB and DC . prove that AD = BC ?

What is CPCT?Give me a detailed brief about cpct?

If the altitudes of a triangle ABC are equal,then prove that triangle is equilateral.

if a+b+c=15 and a2+b2+c2=83 find value of a3+b3+c3-3abc

proof for basic proportionality theorem

  Prove that Sum of Two Sides of a triangle is greater than twice the length of median drawn to third side.

prove that sum of all 3 angles of a triangle is 180.

if x³ + 1/x³ = 110 then find the value of x+1/x

In a triange ABC, prove that AB + AC > 2AD, where AD is the median from A to BC..pls answer this one....

If D is a mid-point of the hypotenuse AC of a right angled triangle ABC ( right angled at B ), prove that BD=1/2 AC

prove that the difference of any two sides of a triangle is less than third side.