Question

(6)
Prove that the two triangles shown below have the same area:
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Answer 1

Step-by-step explanation:

You can figure this one out easily for yourself, but I will tell you that the answer is no.

Here is one counterexample:

I will not draw a picture, so please do that yourself. Draw a line of a convenient length and label it “b” for “base”. Draw a line from one end of “b” and perpendicular to it and label it “h” for “height”. “h” can be shorter, longer, or the same length as “b”. Now connect the free end of “b” and the free end of “h” to each other with a third line. You now have a right triangle whose area is :

A = 1/2 x b x h

Now draw a second diagram as follows: Draw a line “b” the same length as “b” in the first triangle. Draw a line from the midpoint of this new “b” that is perpendicular to “b” and has the same length as “h” in the original triangle. Now draw a line from each end of line “b” in the new diagram to the free end of the new line “h”. The new triangle formed by “b” and these two lines will be an isosceles triangle that looks quite different from the first triangle and thus not congruent to it. But its area will also be:

A = 1/2 x b x h

Same area, different triangles

Answer 2

Answer:

3cm 4 cm triangles same area