All categories

3 years ago

How can you tell if it's a SAS (side angle side) or SSS (side side side) or ASA (angle side angle)?

Mathematics

1 answer:

aliina [53]3 years ago

8 0

The SSS rule states that :

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

The SAS rule states that :

If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.

The ASA rule states that :

If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.

Hope this helps :)

You might be interested in

(3 points) Two friends went fishing. Hilda caught a 16 inch rainbow trout and Bran caught a 23 inch brown trout. Suppose rainbow

wolverine [178]

We are assuming here that the lengths of rainbow trout and brown trout follow a normal distribution, that is, both lengths are normally distributed (which is reasonable for this kind of random variable in populations, like the heights in humans, for example).

Answer:

The rainbow trout resulted longer relative to the corresponding type of fish, that is, one standard deviation above the mean or longer than the 84.134% of the population for rainbow trouts because the brown trout resulted in 0.6 standard deviations above the population for brown trouts (or 72.575% above them).

Step-by-step explanation:

Because both types of fish come from different species, they cannot be fairly compared using the normal distribution of each fish.

Instead, we can compare them if we "transform" these raw data into z-scores in a way that we can use standardized values to determine how far from the mean are the lengths for each fish.

In other words, we have to remember that z-scores tell us the distance of a raw value from the population mean in standard deviations units, no matter the parameters of the normal distribution they coming from. A positive value for the z-score tells us that the raw score is above the population mean, whereas a negative value tells us that the raw score is below it.

We have to remember that the normal distribution is determined by two parameters, namely, the population mean and the population standard deviation.

In the question, we have two lengths coming from two different normal distributions. We can transform them into standardized values so that we can use the standard normal distribution, and then obtain how far from the mean are the lengths for each fish and the percentile that corresponds to this z-score.

The formula for the z-score is

$\\ z = \frac{x - \mu}{\sigma}$ [1]

Where

x is the raw score. In this case, we have two. One is the length of the rainbow trout (16 inches) and the brown trout length (23 inches).

$\\ \mu$ is the population mean for each normal distribution. We also have two. For the rainbow trout mean length, we have a mean of 12 inches, and a mean length of 20 inches for the brown trout.

$\\ \sigma$ is the population standard deviation for each normal distribution. A standard deviation for the rainbow trout of 4 inches, and a standard deviation of 5 inches for the brown trout.

Having all this information at hand, we can proceed to solve the question.

Z-score for rainbow trout

For this case, we have

x = 16 inches.

$\\ \mu = 12$ inches.

$\\ \sigma = 4$ inches.

Using formula [1]

$\\ z = \frac{x - \mu}{\sigma}$

$\\ z = \frac{16 - 12}{4}$

$\\ z = \frac{4}{4}$

$\\ z = 1$

That is, the length of the rainbow trout caught by Hilda is one standard deviation above the mean. If we consult a cumulative standard normal table, we have that

$\\ P(z$

In words, the length for the fish that Hilda caught is, approximately, above than 84.134% of the population for rainbow trouts (one standard deviation above the population mean).

Z-score for brown trout

We can proceed in the same way as we did with the previous case.

For this case, we have

x = 23 inches.

$\\ \mu = 20$ inches.

$\\ \sigma = 5$ inches.

Using formula [1]

$\\ z = \frac{23 - 20}{5}$

$\\ z = \frac{3}{5}$

$\\ z = 0.6$

That is, the length of the brown trout caught by Bran is 0.6 standard deviations units above the mean. With this value at hand, we can conclude that this fish is smaller relative to the type of fish (brown trout) than the rainbow trout caught by Hilda. We can confirm this using the standard normal table:

$\\ P(z$

In words, the length for the fish that Bran caught is, approximately, above than 72.575% of the population for brown trouts (or the length of 72.575% of the population for brown trout are below the length of the brown trout caught by Bran).

In conclusion, the rainbow trout resulted longer relative to the corresponding type of fish, that is, one standard deviation above the mean or longer than the 84.134% of the population for rainbow trouts, because the brown trout resulted in 0.6 standard deviations above the population for brown trouts (or 72.575% above them).

In the graph below, a standard normal distribution (mean = 0, standard deviation = 1), we can confirm the previous result (the red color for the rainbow trout, and the blue color for the brown trout).

8 0

3 years ago

A tank weighs 5.6kg when it 1/4 filled with water.If it weighs 10.4kg when it is full ,what will be it's weight when it is empty

Rzqust [24]

Answer:

4 kg

Step-by-step explanation:

........................

7 0

2 years ago

Read 2 more answers

1. Melissa went to lunch with two friends. She purchased 3 corn dogs, 2 fruit cups, and

umka2103 [35]

Answer:

14 is the answer.

Step-by-step explanation:

8 0

3 years ago

Find the ratio : 1/2 hour to 45 minutes

goldfiish [28.3K]

Answer:

The answer is 2 : 3.

Step-by-step explanation:

First, you have to convert the units to minutes :

1 hr = 60 min

1/2 hr = 60 × 1/2 = 30 min

Then, you have to simplify the ratio to simplest form :

30 : 45

= (30÷15) : (45÷15)

= 2 : 3

3 0

3 years ago

Read 2 more answers

Find the units of displacement (translation) of the point (4,2) to get the image of (7,7). Chapter (transformation) (coordinates

SVEN [57.7K]

Answer:

The rule of the translation will be:

(x, y) → (x+3, y+5)

Step-by-step explanation:

Translation of an object is basically termed as "sliding" the original. If the image is moved right by the 'c' units, the 'c' unit(s) are added to the x-coordinate and if the image is moved left by the 'c' units, the 'c' unit(s) are subtracted to the x-coordinate.

And If the image is moved up by the 'c' units, the 'c' unit(s) are added to the y-coordinate and if the image is moved down by the 'c' units, the 'c' unit(s) are subtracted to the x-coordinate.

As the point is (4, 2)

The image of the point is (7, 7)

As the coordinates of the image point indicate that 3 units are added to the x-coordinate of the original point, and 5 units are added to the ý-coordinate.

Hence, the image will be move 3 units to the right and 5 units up.

Therefore, the rule of the translation will be:

(x, y) → (x+3, y+5)

(4, 2) → (x+3, y+5) = (4+3, 2+5) = (7, 7)

3 0

3 years ago