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3 years ago

Explain why the Leg-Leg (LL) theorem is the same as the Side-Angle-Side (SAS) postulate.

2 answers:

8 0

Both claim that if the two legs (the sides of the right triangle which meet to form 90°) and one of the corresponding acute angles of two right triangles are congruent then the two right triangles are also congruent :) They say the same but in a slightly different way!

Marysya12 [62]3 years ago

3 0

Answer:

SAS postulate of congruence refers to the congruence between two pairs of corresponding sides and the congruence between one pair of corresponding angles which are formed by the two sides.

Notice that to use this postulate we just need three congruent elements of those triangles.

Similarly we have the Leg-Leg theorem which is used to demonstrate congruence between right triangles. Using this theorem would give the same result than using SAS postulate, because Leg-Leg theorem is actually based on that.

In other words, we can use LL theorem for congruence because all right triangles has a congruent angle, the right angle. So, basically, when you use the LL theorem, you are actually use the SAS postulate indirectly.

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Use the substitution method to solve the system of equations. choose the correct ordered pair. 2x - y = 103x - 2y = 8

crimeas [40]

$2x-y=10\Rightarrow 2x-10=y \\ 
\Longrightarrow 3x-2y=8\Rightarrow 3x-2(2x-10)=8 \\ 
3x-4x+20=8 \\ -x=8-20=-12 \\ x=12 \\ \\ y=2(12)-10=24-10 \\ y=14 \\ \\ (x,y)=(12,14)$

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3 years ago

The sum of three certain consecutive numbers is 240. Find the 3 numbers.

BartSMP [9]

Answer:79 , 80 , 81

Step-by-step explanation:What three consecutive integers have a sum of 240? What three consecutive integers have a sum of 240? Which means that the first number is 79, the second number is 79 + 1 and the third number is 79 + 2. Therefore, three consecutive integers that add up to 240 are 79, 80, and 81.

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3 years ago

A container in the shape of a rectangular prism holds 651.168 cubic inches when completely filled with water. The container has

serg [7]

Answer : 3.4

Explanation: 12.6 x 15.2= 191.52
651.168 / 191.52 = 3.4

3 0

3 years ago

Question 5: prove that it’s =0

mamaluj [8]

Answer:

Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that $\cos(\frac{2}{x})$ is a variable number between -1 and 1 (inclusive).

This means that $-1 \le \cos(\frac{2}{x}) \le 1$ .

$x^4 \ge 0$ for all value $x$ . So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

$-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

By squeeze theorem, if $-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4$

and $\lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L$ , then we can also conclude that $\im_{x \rightarrow} x^4\cos(\frac{2}{x})=L$ .

So we can actually evaluate the "if" limits pretty easily since both are continuous and exist at $x=0$ .

$\lim_{x \rightarrow 0}x^4=0^4=0$

$\lim_{x \rightarrow 0}-x^4=-0^4=-0=0$ .

We can finally conclude that $\lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0$ by squeeze theorem.

Some people call this sandwich theorem.

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3 years ago

Draw a rectangle that has an area of 8 units square and a perimeter of 12 units. What are the side lengths

choli [55]

Answer:

4 by 2

Step-by-step explanation:

you can basically guess and check with this question but I knew if it was a rectangle then 2 sides would be larger than the other. So I started off figuring out what times what equals 8 and I got 2 and 4. So I put those in for the side lengths and I got 12.

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3 years ago