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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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Please help and explain!!!!!
FinnZ [79.3K]

Let x be the amount of the 30% alloy and y the amount of the 60% alloy the metalworker will use. However much is used, the final alloy will have a mass of

x+y=100

kilograms. For each kg of the 30% alloy used, 0.3 kg is copper; similary, each kg of the 60% alloy contributes 0.6 kg, so that

0.3x+0.6y=0.54(x+y)=54

Now,

x+y=100\implies y=100-x

\implies0.3x+0.6(100-x)=54

\implies60-0.3x=54

\implies0.3x=6

\implies x=20

\implies y=100-20=80

6 0
3 years ago
Less than 75% of workers got their job through internet resume sites. A researcher thinks it has increased.
Vera_Pavlovna [14]

Answer:

H0 : p = 0.75  against    H1: p > 0.75  One tailed test.

Step-by-step explanation:

We state our null and alternative hypotheses as

H0 : p = 0.75  against    H1: p > 0.75  One tailed test.

In this case H0 is not defined as p≤ 0.75 because the acceptance and rejection regions cannot be set up. Therefore we take the exact value of H0 : p= 0.75.

The claim is that the probability of the workers getting their job through the internet is greater than 75% or 0.75.

As H0 is supposed to be less than we choose H1 to be greater than equality.

5 0
3 years ago
A garden is rectangular with an area of 6/7 square miles. If the length of the garden is 3/5 miles, what is its width?
Dafna11 [192]

Answer:

Step-by-step explanation:

Area= length x width

area=6/7, length=3/5, width=?

6/7=3/5 x width

6/7 divided by 3/5= 6/7 x 5/3 (you have to multiply by the recipricol, or flip the fraction.)

6/7 x 5/3=30/21= 1 3/7=width

7 0
3 years ago
Ben earns a salary of $120 a week plus $25 for each table he sells at
gtnhenbr [62]

Answer:

add 25 each time and count how many times you add it on

Step-by-step explanation:

and that will be your answer

7 0
2 years ago
out of 30 questions on the maths test tomi knew the answer to 27 of them what percentage of questions did tomi know the answer f
Vedmedyk [2.9K]

Answer:

90

Step-by-step explanation:

\frac{27}{30}  \times 100

so after we cut the nessecary we get 90%

Hope this helps you

Mark as the brainlist

thank you

8 0
2 years ago
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