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disa [49]
3 years ago
6

Based on the information marked in the diagram, ABC and DEF must be congruent.

Mathematics
2 answers:
ziro4ka [17]3 years ago
7 0
Hello!

As you can see, both AB and DE both have one dash mark. This means they are congruent. Angles C and F are congruent as well. A and D both have right angles. These triangles are congruent.

I hope this helps!
drek231 [11]3 years ago
3 0

Answer:

Option A is correct

True, ΔABC and ΔDEF must be congruent.

Explanation:

LA theorem or Postulates states that given two right triangles,  where one acute angle and a leg of one of the triangles are congruent to  an angle and a leg of the other triangle, then the two triangles are congruent.

In  ΔABC and ΔDEF

AB = DE              [Leg]                [Given in the figure]

\angle BAC = \angle EDF = 90^{\circ}     [Given]

\angle BCA = \angle EFD   [Acute angle]        [Given in the figure]

Then, by the LA theorem or Postulates;

therefore, ΔABC \cong ΔDEF .





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Can someone please explain how the answer is D
Kitty [74]

Step-by-step explanation:

Because the length of ST is calculated using pythagorean theorem:

{c}^{2}  =  {a}^{2}  +  {b}^{2}

Where the square of the hypotenuse is equal to the sum of squares of the other two sides of a right triangle. In this case, the hypotenuse is ST and the other two sides are distances between S and T over the X and Y axis. Those are easily calculated:

x =  |sx - tx|  \\ y =  |sy - ty|

Where x is the distance between S and T over X axis and Y distance over Y axis, sx and tx are X coordinates of S and T, sy and ty are Y coordinates of S and T.

Using that formula, you get that y = 17 and x = 8.

Back to the pythagorean theorem, if we put those number in the formula of the pythagorean theorem, we get something like this:

{c}^{2}  =  {x}^{2}  +  {y}^{2} \\  {c}^{2}  =  {8}^{2}  +  {17}^{2} = 64 + 289  \\  {c}^{2}  = 353 \\ c =  \sqrt{353}

And finally, the correct answer is in fact 353.

3 0
3 years ago
What is the answer to this question
Ratling [72]
Hello!

As you cans see, the angle is a right angle, which measures 90°. One of the angles measure 35°

90 - 35 = 55

That means 5x = 55°

Divide both sides by 5

\frac{5x}{5} =  \frac{55}{5}

\framebox{x = 11 \°}
7 0
3 years ago
Read 2 more answers
Help me please ASAP
Kryger [21]
Its 160 .................
7 0
3 years ago
Read 2 more answers
What is 19 divided by 20 using long division & decimals?
andrew-mc [135]

Answer:

0.95

(Don't have paper, because I accidentally threw away paper )

3 0
2 years ago
After 3 minutes, a submarine had descended to −320 feet. After 8 minutes, the submarine had descended to −420 feet. Assuming a l
LiRa [457]

Answer:

d(t) = -20t - 260

Step-by-step explanation:

The depth function is:

d(t) = mt + b

After 3 minutes, a submarine had descended to −320 feet.

This means that d(3) = -320. So

d(t) = mt + b

-320 = 3m + b

After 8 minutes, the submarine had descended to −420 feet.

This means that d(8) = -420. So

d(t) = mt + b

-420 = 8m + b

From the first equation:

b = -320 - 3m

So

-420 = 8m + b

-420 = 8m - 320 - 3m

5m = -100

m = \frac{-100}{5}

m = -20

And

b = -320 - 3*(-20) = -260

So

d(t) = -20t - 260

7 0
3 years ago
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