Home
Class 9
MATHS
If A. B and C are three points on a lin...

If A. B and C are three points on a line, and B lies between A and C then prove that `A B+B C=A C`.

Text Solution

AI Generated Solution

To prove that \( AB + BC = AC \) when points A, B, and C are collinear and B lies between A and C, follow these steps: ### Step-by-Step Solution: 1. **Identify the Points on the Line**: Let A, B, and C be three points on a straight line such that B is between A and C. 2. **Visual Representation**: ...
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO EUCLIDS GEOMETRY

    NCERT ENGLISH|Exercise Exercise 5.2|2 Videos
  • INTRODUCTION TO EUCLIDS GEOMETRY

    NCERT ENGLISH|Exercise Exercise 5.1|7 Videos
  • HERONS FORMULA

    NCERT ENGLISH|Exercise Solved Examples|6 Videos
  • LINEAR EQUATIONS IN TWO VARIABLES

    NCERT ENGLISH|Exercise Exercise 4.1|2 Videos

Similar Questions

Explore conceptually related problems

If A, B and C are three poins on a line and B lies between A and C, then prove that AB + BC = AC.

If A, B and C are three sets such that A cup B = A cup C and A cap B = A cap C , then prove that B = C .

If a point C lies between two points A and B such that A C=B C , then prove that A C=1/2A B . Explain by drawing the figure.

If A,B and C are three sets such that A cup B = C and A cap B = phi , then prove A = C - B .

If A ,\ B and C are three matrices of the same order, then prove that A=B=>A+C=B+C .

In A B C , if B D_|_A C and B C^2=2\ A C C D , then prove that A B=A C .

In Figure, A B C D is a parallelogram. E and F are the mid-points of the sides A B and C D respectively. Prove that the line segments A F and C E triset (divide into three equal parts) the diagonal B Ddot

A ,\ B ,\ C ,\ D are four consecutive points on a circle such that A B=C Ddot Prove that A C=B D

In Figure, lines A B\ a n d\ C D are parallel and P is any point between the two lines. Prove that /_A B P+/_C D P=\ /_D P B

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .