# MATHS

posted by .

Four points lie in a plane. They are partitioned into two pairs so that the sum of the lengths of the segments joining the points of each pair has the minimal possible value.
Prove that these segments have no common points.

• MATHS -

Let segments AB and CD have common point E. Then AC<AE+EC and BD<BE+ED.
AE+EC+BE+ED=AB+CD

## Similar Questions

1. ### geometry

We are learning about proofs. We drew lines between noncollinear points. Our table showed 2 points >> 1 line segment, 3 point >> 3 line segments, 4 points >> 6 line segments, 5 points >> 10 line seg, 6 points …
2. ### math

you can draw one segment to connect two points and three distinct segments to connect three named points. how many segments can you drawto connect five points if no three of the points lie on the same line.........please help me i …
3. ### math

you can draw one segment to connect two points and three distinct segments to connect three named points. how many segments can you drawto connect five points if no three of the points lie on the same line.........please help me i …
4. ### geometry

M and N are the midpoints ofandrespectively. Using graph paper, repeat this process from the last problem using different coordinates for P, Q, and R. How do these lengths MN and PQ compare now?
5. ### Geometry

M and N are the midpoints ofandrespectively. Using graph paper, repeat this process from the last problem using different coordinates for P, Q, and R. How do these lengths MN and PQ compare now?
6. ### geometry

Trisha drew a pair of line segments starting from a vertex. Which of these statements best compares the pair of line segments with the vertex?
7. ### maths

A point P is uniformly chosen inside a regular hexagon of side length 3. For each side of the hexagon a line is drawn from P to the point on that side which is closest to P. The probability that the sum of the lengths of these segments …
8. ### math

Ten distinct noncollinear points are chosen on a plane. a) How many line segments can be formed by joining any two of these points?
9. ### Math

We are learning about proofs. We drew lines between noncollinear points. Our table showed 2 points >> 1 line segment, 3 point >> 3 line segments, 4 points >> 6 line segments, 5 points >> 10 line seg, 6 points …
10. ### math

X1, X2,...,X9 are nine points on the circumference of circle O. Line segments are drawn connecting each pair of points. What is the largest number of different points inside the circle at which at least two of these line segments intersect?

More Similar Questions