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Natasha_Volkova [10]
3 years ago
13

Which of the following statements are enough to prove that triangles EFI and GFH are similar?

Mathematics
2 answers:
SCORPION-xisa [38]3 years ago
6 0

To Prove: ΔEFI ~ Δ GFH

Proof:

When two triangles are similar, their corresponding sides are Proportional and their corresponding interior angles are equal.

Two Triangles can be proven similar by following Similarity Criterion.

1. AA

2.SSS

3.SAS

→∠EFI=∠GFH-------[Vertically Opposite angles]

The Other statement which is needed to prove that triangles EFI and GFH are similar is

 Option C:→  ∠E ≅ ∠G

So, Two triangles ΔEFI and Δ GFH are Similar by Angle-Angle(AA) Criterion.

baherus [9]3 years ago
3 0

Answer:

<h2>C. ∠E ≅ ∠G</h2>

Step-by-step explanation:

When we have to demonstrate a similarity between triangles, we don't use congruence postulates, because similarity is different that congruence. When we talk about similarity, we are using proportions. So, two similar triangles are proportional, not equal, this means that sides are not equal, only proportional, but angles between triangle are equal.

So, in this case, option C offers enough to prove a similarity. They are equal because they are alternate interior angles. Also, the common vertex F make angles EFI and GFH equal too, because those are opposite angles. At last, angle H and angle I are also equal, because if two angles are equal, the third also it is.

Therefore, as you can see, option C gives a window to a demonstration. So, based on this reasoning, we can say that both triangles are similar by Angle-Angle postulate.

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A car travelled 72 km in 3/4 h. If the car is travelling at a constant rate how far will the car travel in one hour?
Anvisha [2.4K]

Answer:

96 km

Step-by-step explanation:

72/3 is 24. When yo add 24 to 72 you get 96km.

3 0
3 years ago
Solve the equation f/6= 2.5
dezoksy [38]

Answer:

f=15

Step-by-step explanation:

f/6=2.5

f=2.5*6

f=15

3 0
3 years ago
What is the slope of the equation 3x - 4y = 32?<br> -3/4<br> -8<br> 3/4<br> 8
Thepotemich [5.8K]

Answer:

y=34x−8

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
12x+16y=-15 in slope intercept form ? please help
Firlakuza [10]

Answer: y = -3/4x - 15/16

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Hope this helps you out! ☺

6 0
3 years ago
An unfair coin with​ Pr[H] = 0.2 is flipped. If the flip results in a​ head, a marble is selected at random from a urn containin
satela [25.4K]
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2. 
H - head 
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T)   = 0.8
urn
3 red and 5 blue

when heads is obtained 
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12

when tails is obtained 
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3

using bayes rule the answer can be found out, 
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
               = 0.12 / (0.12 + 0.3)
               = 0.12 / 0.42
               = 0.286
the final answer is 0.286
6 0
3 years ago
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