Question

Given: the medians divide a triangle into 6 smaller triangles.

Prove: The area of all the triangles are the same

Answer #1

Median of a triangle divides the triangle into two triangles with equal area.

For consider and median . We got two triangles here and . Now both the triangles have bases namely and respectively and they're of equal length. Also height of both the triangles is equal. .

Now, are medians of triangles respectively.

So

Also has medians .

Hence, the area of all the 6 triangles is the same.

Let △ ??? be a triangle with centroid ? and medians ??′, ??′,
and ??′. Prove that the six triangles △ ??′?, △ ???′, △ ??′?, △
???′, △ ??′?, and △ ???′ all have equal areas.
Please prove with an image and numbered style

Prove: If the sides of a right triangle have integer lengths and
the area of the triangle equals its perimeter, then the sides
either have lengths 6, 8, and 10, or have lengths 5, 12 and 13.

Prove that equilateral triangles exist in
neutral geometry (that is, describe a construction
that will yield an equilateral triangle). note that all the
interior angles of an equilateral triangle will be congruent, but
you don’t know that the measures of those interior angles is
60◦.Also, not allowed to use circles.

For all integers a,b , c prove that if a doesn't divide then a
doesn't divide b and a doesn't divide c

two sides and an angle (ssa) of a triangle are given.
Determine whether the given measurement produce one triangle, two
triangles, or no triangle at all. a=12, b=13.8, A=47

Use calculus to find the area A of the triangle with
the given vertices.
(0, 0), (4,
1), (1, 6)
A =

Use calculus to find the area A of the triangle with
the given vertices.
(0, 0), (4,
2), (2, 6)

An isosceles triangle has a base of 6 units and an area of 36 square units. Find the dimensions of the rectangle with the largest area that can be placed inside the triangle, with one of the sides at the base of the triangle.

Use the Law of Sines to solve for all possible triangles that
satisfy the given conditions. (If an answer does not exist, enter
DNE. Round your answers to one decimal place. Below, enter your
answers so that ∠A1 is smaller than
∠A2.)
b = 26, c = 31, ∠B
= 27°
∠A1 =
°
∠A2 =
°
∠C1 =
°
∠C2 =
°
a1 =
a2 =

An
isosceles triangle has a base of 6 units, and an area of 36 units
squared. Find the dimensions of the rectangle with the maximum area
that can be put into the triangle, with one of its sides in or at
the base of the triangle mentioned. (Optimization problem) Help!
thank you.

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