midpoint of a triangle?

Question

If the midpoints of the sides of a triangle are connected, the area of the triangle formed is what part of the area of the original triangle?

Answer 1

The line connecting the midpoints of two sides of a triangle is || to the 3rd side and = to 1/2 its length.

Therfore the triangle formed by connecting all three midpoints is similar to the original triangle and has each of its sides equal to 1/2 of the corresponding sides of the original triangle.

hence its area is 1/4 that of the original triangle

Answer 2

Yes, it is 1/4 the original area, because it will separate the Big triangle into 4 small ones, each with 1/4 the total area.

Props to mikagami715 for getting it right first.

Answer 3

E is the midpoint of BC and CE = 7, so BE = 7 F is the midpoint of CA and AF = 6, so CF = 6 the fringe, he distance around the fringe of the triangle is 36, so AB + BC + CA = 36 BE = 7 and EC = 7, so BC = 14 CF= 6 and FA = 6, so CA = 12 So then we plug this into the fringe formula: AB + BC + CA = 36 AB + 14 + 12 = 36 AB = 10 Now all individuals understand D is the midpoint of AB and AB = 10, so ad would properly be 5.

Answer 4

You get 4 congruent triangles when this happens so the new triangle is 1/4 of the original.

Answer 5

its always 1/4 of the area of the original triangle..

Answer 6

half the area of the original triangle

Answer 7

Use a coordinate plane (graph paper).
A(0,0) and B(b,0) and C(0,c)
with midpoints
D(b/2,c/2) and E(b/2,0) and F(0,c/2)
After connecting the points, you get two right traingles with areas: bc/2 and bc/8
[ bc/8 ] / [ bc/2 ]
[ bc/8 ][ 2/bc ]
[ 1/4 ]

Answer 8

I'm no mathemetician, but it seems to me the three lines would intersect...the area they comprise would be zero.

Answer 9

the hypotnuse??