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1 year ago

Which shows two triangles that are congruent by ASA

Mathematics

2 answers:

Ksenya-84 [330]1 year ago

7 0

The four options are attached below

Answer:
Second attachment is the correct choice

Explanation:
ASA (angle-side-angle) means that two angles and the included side between them in the first triangle are congruent to the corresponding two angles and the included side between them in the second triangle

Now, let's check the choices:
First attachment:
It shows that two sides and the included angle between them in the first triangle is congruent to the corresponding two sides and the included angle between them in the second one. This is congruency by SAS. Therefore, this option is incorrect

Second attachment:
It shows that two angles and the included side between them in the first triangle is congruent to the corresponding two sides and the included angle between them in the second triangle. This is congruency by ASA. Therefore, this option is correct

Third attachment:
It shows that the three angles in the first triangle are congruent to the corresponding three angles in the second one. This is not enough to prove congruency. Therefore, this option is incorrect

Fourth attachment:
It shows that the three sides in the first triangle are congruent to the corresponding three sides in the second one. This is congruency by SSS. Therefore, this option is incorrect.

Based on the above, the second attachment is the only correct one

Hope this helps :)

Ray Of Light [21]1 year ago

7 0

The second one, as shown in the attached picture.

<h3>Further explanation</h3>

The ASA (Angle-Side-Angle) postulate for the congruent triangles: two angles and the included side of one triangle are congruent to two angles and the included side of another triangle; the included side properly represents the side between the vertices of the two angles.
The SAS (Side-Angle-Side) postulate for the congruent triangles: two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle; the included angle properly represents the angle formed by two sides.
The SSS (Side-Side-Side) postulate for the congruent triangles: all three sides in one triangle are congruent to the corresponding sides within the other.
The AAS (Angle-Angle-Side) postulate for the congruent triangles: two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

- - - - - - - - - -

Notes

The angle-side-side postulate for the congruent triangles doesn't exist because an angle and two sides don't guarantee that two triangles are congruent. If two triangles have two congruent sides and a congruent non-included angle, then triangles don't seem to be necessarily congruent. This can be why there's no side-side-angle (SSA) and there's no angle-side- side postulate.
The AAA (angle-angle-angle) postulate for congruent triangles does not work because having three corresponding angles of equal size is not enough to prove congruence. This principle is usually used for the similarity of two triangles.

<h3>Learn more</h3>

About the lengths of the legs of the triangle brainly.com/question/13027296
About vertical and supplementary angles brainly.com/question/13096411
Calculate the measures of the two angles in a right triangle brainly.com/question/4302397

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Answer:

Step-by-step explanation:

(a)

The bid should be greater than $10,000 to get accepted by the seller. Let bid x be a continuous random variable that is uniformly distributed between

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$=1- \frac{[15000-12000]}{5000}\\\\=1-0.6\\\\=0.4$

(b) The interval of the accepted bidding is [$10,000,$15,000], where b = $15,000 and a =$10,000. The interval of the given bidding is [$10,000,$14,000].

$\begin{array}{c}\\P\left( {X{\rm{ < 14,000}}} \right){\rm{ = }}1 - P\left( {X > 14000} \right)\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{14000}^{15000}\\\end{array} P(X14000)$

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(c)

The amount that the customer bid to maximize the probability that the customer is getting the property is calculated as,

The interval of the accepted bidding is [$10,000,$15,000],

where b = $15,000 and a = $10,000. The interval of the given bidding is [$10,000,$15,000].

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(d) The amount that the customer bid to maximize the probability that the customer is getting the property is $15,000, set by the seller. Another customer is willing to buy the property at $16,000.The bidding less than $16,000 getting considered as the minimum amount to get the property is $10,000.

The bidding amount less than $16,000 considered by the customers as the minimum amount to get the property is $10,000, and greater than $16,000 will depend on how useful the property is for the customer.

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If cyanide in a stream next to a gold mine increases from 240 ppm to 360 ppm, what percent increase is this?

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Given :

Initial concentration , 240 ppm .

Final concentration , 360 ppm .

To Find :

Percent increase.

Solution :

Percentage increase is given by :

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Therefore , percent increase is 50 % .

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1 year ago

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Answer:

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Step-by-step explanation:

The random variable X is defined as the age at death of a randomly selected indoor cat.

(a)

The distribution of X is:

$X\sim N(\mu = 16, \sigma^{2}=2.5^{2})$

(b)

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$=P(0.48$

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(c)

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