any body tell me mid point theoram plz.?

Answer 1

__________________________________________________
__________________________________________________

MIDPOINT THEOREM:

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side.
_____________________________________________________

PROOF:

We first write the statement of the theorem in the form “If …, then …”:

If D and E are the midpoints of sides AB and AC of respectively, then

(1) DE // BC, (2) .

We need to prove that the conclusions (1) and (2) hold.

The strategy is to show that the two triangles and are similar. Then apply the properties of similar triangles to prove what we need.

STATEMENTS:

1. m

2. |AB| : |AD| = 2, |AC| : |AE| = 2

3. and are similar

4.

5. DE // BC

6. |DE| : |BC| = |AD| : |AB| = 1/2

7.

REASONS:

1. Same angle

2. Given

3. SAS-similarity

4. Corresponding angles of similar triangles.

5. Corresponding angles are equal.

6. By (2) and (3).

7. By (6).
__________________________________________

Example 1

Suppose that in the following figure, points D and E are the midpoints of AB and AC respectively, and AE = 2.51cm.

Find and ||.


Recall that we have seen the following in Chapter 3 Activity 6 (Midpoint Quadrilateral), we provide a proof using Midpoint Theorem here.
__________________________________________

Example 2

Given a quadrilateral HIJK, let L, M, N, and O denote the respective midpoints. Show that LMNO is a parallelogram.
__________________________________________

Example 3

Suppose that the triangle is an isosceles triangle where |AB | = |BC | and D, E and F are midpoints of the sides AB, BC and AC respectively.

Show that is isosceles as well.
________________________________________

DISCUSSION:

Suppose in the following figure,

(1) Can you prove DE // BC?

(2) What is |DE|:|BC| ?

(3) What is the general conjecture you can

made based on the Midpoint Theorem

and the answers to parts (1) and (2)?
___________________________________________________

http://66.218.69.11/search/cache?p=math+%22midpoint+theorem%22+definition&ei=UTF-8&fr=ks-ans&x=wrt&u=math.nie.edu.sg/tangwk/DSM101/SKII%252006%2520Chapter5.doc&w=math+%22midpoint+theorem%22+definition&d=QNmGcZIFNnSS&icp=1&.intl=us
___________________________________________________

(Segments and Rays)

THE MIDPOINT THEOREM: ( The Definition of Midpoint)

Given AB, its midpoint M is:
2AM = AB and AM = ½ AB
2MB = AB and MB = ½ AB


A perpendicular bisector of a segment is a line, ray or another segment that is perpendicular to the segment at its midpoint.

Theorem:
If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

Theorem:
If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.
___________________________________________________

http://library.thinkquest.org/10030/2themid.htm
___________________________________________________

Answer 2

In a triangle, the line segment joining the mid-points of any two sides is parallel to the third side and is half of it.
So if we have a triangle ABC and a line intersects AB and AC at D and E respectively, then DEIIBC and DE=BC/2

Answer 3

The midpoint of a line segment in coordinate geometryy is given by the formula:
{ (|x1-x2|) /2, (|y1-y2|) /2 } <---- x1, x2, y1, & y2 should be read as "x sub 1," etc. since I'm not clear how to do subscripts in a web text box.

Essentially, the formula above simply takes the average of the 2 x values and the average of the 2 y values to find x and y coordinates of the midpoint.

Answer 4

the midpoint is m=
[(the second x - the first x) divided by 2, (the second y - the first y) divided by 2)

example - the points are (1,3) and (7,5)

so you do (7-1) and (5-3)

you divde both by two

so 6/2 =3 and 2/2 =1

so the mid point is (3,1)

Answer 5

MIDPOINT THEOREM:-

Consider an arc AB(can be explained clearly with a major arc) of a circle.
Let P be the midpoint of arc AB(major arc). Take any point C on the circumference of the circle. Join AC and BC. Draw PD perpendicular to AC. Then, AD=DC+BC

Answer 6

The Midpoint Theorem: ( The Definition of Midpoint)

Given AB, its midpoint M is:
2AM = AB and AM = AB
2MB = AB and MB = AB

Hope I helped!
10 points for best answer?

Answer 7

midpoint theorem states that the line passing throuhg the midpoint of two sides of triangle is parallel to the third side

Answer 8

Theorem:
If a point lies on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.

Theorem:
If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

Answer 9

midpoint theorem states that the line passing throuhg the midpoint of two sides of triangle is parallel to the third side

Answer 10

If the starting point of a line is x1 & end point is x2 then the mid point of line is (x1+x2)/2