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jolli1 [7]
3 years ago
8

Which two angles are congruent

Mathematics
1 answer:
Anna35 [415]3 years ago
5 0
Angles FED and angle JKL
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Line l is parallel to line e in the figure below.
agasfer [191]

Answer: The correct option are as follows;

(1) The triangles are similar because corresponding sides are congruent

(2) The triangles are similar because alternate interior angles are congruent

(3) In the similar triangles, Angle 3 and Angle 6 are corresponding angles

Step-by-step explanation: Please refer to the picture attached for details.

The line i and line e has been drawn and marked as parallel lines. Also two transversal lines m and n have been drawn to intersect in the region between the parallel lines to form two triangles (as shown in the picture).

From the information given, where line e intersects with line n we have angle 1, and where line e intersects with line m we have angle 3, and then the third angle is angle 2.

Furthermore, where line l intersects line m we have angle 6, and where line l intersects line n is angle 4. Also in this second triangle, the third angle is 5.

Upon close observation we would see that Angle 6 is equal to Angle 3, since the transversal m has cut across both parallel lines l and e. Similarly Angle 4 is equal to Angle 1 since the transversal n has cut across parallel lines l and e. Having that Angles 3 and 1 are congruent to Angles 6 and 4, we can conclude that the value of the third angle in one triangle is equal to the that of the third in the second triangle, that is, Angle 2 equals Angle 5. Also, if the angles are similar and the lines l and e are parallel, then the lines formed in both triangles are equal.

So our conclusions are;

The interior angle are alternate angles (Angles 3 and 6, Angles 1 and 4), and the third interior angles are Opposite (Angles 2 and 5 {Opposite angles are equal})

8 0
2 years ago
Read 2 more answers
Consider this expression
Sloan [31]

Answer:

\displaystyle \large{(x + 9)(x - 8)}

The value of a is 9 and b is -8

Step-by-step explanation:

\displaystyle  \large{(x + a)(x  + b) =  {x}^{2}  + (a + b)x + ab}

We need to find two numbers that add up or subtract off to 1.

Then we also use the same two numbers that multiply and get -72.

Let's see:-

  • 9 and -8 seem like correct values.

Because 9+(-8) is 9-8 = 1

And 9(-8) is -72.

Therefore:

\displaystyle \large{ {x}^{2}  + x - 72 = (x + 9)(x - 8)}

The value of a is 9 and the value of b is -8 according to form of (x+a)(x+b)

8 0
2 years ago
Read 2 more answers
This box is a right rectangular prism. Its dimensions are 3 inches by 3 inches by 11 inches.
Makovka662 [10]

Answer:

Stot = 150 in2

Step-by-step explanation:

there is your anser

4 0
3 years ago
Read 2 more answers
HELP ASAP!!!! <br> EXTRA POINTS!!
-BARSIC- [3]

20%. total= 5 => total= 25

8 0
3 years ago
Given a standard deck of 52 cards, 3 cards are dealt without replacement. Using this situation, answer the questions below.&lt;b
kherson [118]
Given that <span>3 cards are dealt without replacement in a </span><span>standard deck of 52 cards.

Part A:

There are 4 queens in a standard deck of 52 card, thus the probability that the first card is a queen is given by 4 / 52 = 1 / 13.

Since, the first card is not replaced, thus there are 3 queens remaining and 51 ards remaining in total, thus the probability that the second card is a queen is given</span> by 3 / 51 = 1 / 17

Similarly the probability that the third card is a queen is given by 2 / 50 = 1 / 25.

Therefore, the probability that <span>all three cards are queens is given by

\frac{1}{13} \times \frac{1}{17} \times \frac{1}{25} = \frac{1}{5525}



Part B:

Yes the probability of drawing a queen of heart is independent of the probability of drawing a queen of diamonds because they are separate cards and drawing one of the cards does not in any way affect the chance of drawing the other card.



Part C:

Given that the first card is a queen, then there are 3 queens remaining out of 51 cards remaining, thus the number of cards that are not queen is 51 - 3 = 48 cards.

Therefore, </span>if the first card is a queen, the probability that the second card will not be a queen is given by 48 / 51 = 16 / 17



Part D:

<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining.

Therefore, </span>if two of the three cards are queens ,<span>the probability that you will be dealt three queens</span> is given by 2 / 50 = 1 / 25 = 0.04



Part E:

<span>Given that the first two card are queens, then there are 2 queens remaining out of 50 cards remaining, thus the number of cards that are not queen is 50 - 2 = 48 cards.

Therefore, </span>if two of the three cards are queens ,the probability that the other card is not a queen is given by 48 / 50 = 24 / 25 = 0.96
8 0
3 years ago
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