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2 years ago

Given points A(−2,0), B(−5,3), C(−9,−1), P(7,6), Q(4,0), and R(−4,4), which of the following proves that △ABC~△PQR?

Mathematics

1 answer:

UNO [17]2 years ago

7 0

Based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).

<h3>The SSS Similarity Theorem</h3>

Two triangles having three pairs of sides that are proportional can be proven to be similar by the SSS similarity theorem.

If the triangle ABC and triangle PQR are similar, their corresponding sides will be proportional, meaning that: AB/PQ = BC/QR = CA/RP.

Therefore, using the distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ , the sides of each triangle is found.

Therefore, it shows that:

AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5

Therefore, based on the SSS similarity theorem, △ABC ~ △PQR because AB/PQ = BC/QR = CA/RP = √2/√5 = √10/5 (option D).

Learn more about the SSS similarity theorem on:

brainly.com/question/4163594

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3 years ago

If M is the set of all square of integers that are less than 100 and N is the set of all positive even numbers that are under 30

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a) X = {e , i , g , h , t , y}

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X ∩ W = {e , t , y}

Step-by-step explanation:

* Lets explain how to solve the problem

- We can find a square number by multiply the number by itself

- M is the set of all square integers that are less than 100

∵ The integers from -9 to 9 has square less than 100

∴ M = {0 , 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81}

- N is the set of all positive even numbers that are under 30

∵ Even number any number divisible by 2

∵ They are positive numbers

∴ They start with 2 because zero is not a positive or negative

∴ N = {2 , 4, 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 , 28}

- M ∩ N means the common numbers between set M and set N

∵ The common elements of M ∩ N are square and even less

than 30

∴ M ∩ N = {4 , 16 }

- M ∪ N means all the elements in M and N without reputation

∴ M ∪ N = {0 , 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 25 ,

26 , 28 , 36 , 49 , 64 , 81}

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∵ The letters of word seventy are s e v e n t y

∵ We don't repeat any element in the set

∴ W = {e , n , s , t , v , y}

- X ∪ W means all the elements in X and W without reputation

∴ X ∪ W = {e , i , g , h , n , s , t , v , y}

- X ∩ W means the common elements between set X and set W

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3 years ago

Please help. thanks.

Free_Kalibri [48]

Hello!

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Hope this helps!

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