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Vlad1618 [11]
3 years ago
13

Explain why drawing both diagonals on any rectangle will always result in two pairs of nonoverlapping congruent triangles.

Mathematics
1 answer:
raketka [301]3 years ago
7 0

Answer:

It is because not all sides of a rectangle are equal in length; unlike a square.

Step-by-step explanation:

Let's start by drawing the first diagonal.

You know already how a rectangle looks. It has 4 sides and 2 sets of parallel sides. Each pair of parallel sides has the same length.

A diagonal is a line crossing from one edge of a four-sided shape to the opposite edge; such that it divides the shape into two equal halves.

Now place your rectangle horizontally. Let the two longer sides be on the horizon while the two shorter sides go vertical.

We draw the first diagonal from the edge on the top right to the opposite edge (down left). This will divide the shape into two equal halves and each half will be a triangle; a congruent one at that.

When you fold this rectangle along its diagonal, the two triangles will not overlap! The resulting shape will be like two triangular mountains lying side by side. You can use a paper (cut in the shape of a rectangle) for this experiment.

Why does this happen, instead of the two triangles covering each other (overlapping)?

This happens because a rectangle doesn't have 4 equal sides. Check out a square and you'll see that both triangles will overlap after a diagonal is drawn across the square.

Draw the second diagonal of the rectangle (from up-left to down-right) and the same thing is observed.

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Challenge Yossi used to have a square garage with 246 ft of floor space. recently built an addition to it. The garage is still a
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Considering the perimeter of a square, it is found that:

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  • The length of one side of the garage​ now is of 92.25 ft.
  • The percent increase in the length of one​ side was of 50%.

<h3>What is the perimeter of a square?</h3>

The perimeter of a square of side length s is given by four times the length, that is:

P = 4s.

Before the change, the perimeter was of 246 ft, hence:

4s = 246

s = 246/4

s = 61.5.

The length of one side of the garage​ originally was of 61.5 ft.

After that, the perimeter increased by 50%, hence:

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4s = 369

s = 369/4

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The length of one side of the garage​ now is of 92.25 ft.

The percent increase is the increase divided by the initial value, hence:

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The percent increase in the length of one​ side was of 50%.

More can be learned about the perimeter of a square at brainly.com/question/10489198
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