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3 years ago

Given: ABCD is a ∥-gram; DE ∩ AB =F Prove: △ADF∼△CDE

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

5 0

Answer:

By AA similarity

Step-by-step explanation:

We have been given that ABCD is a parallelogram

So, by the property of parallelogram AB ||CD and FD is cutting the line BC

Hence, FD is transverse line. In transverse line alternate angles are equal.

Therefore, ∠AFD=∠EDC (alternate interior angles)

And ∠FAD=∠ECD (opposite angles in parallelogram)

Therefore, by AA similarity △ADF∼△CDE

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Tom's age is 5 more than twice Dic's age.

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What is the correct order of these numbers ... 5/6, 12/13, 0.8

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8090 [49]

Answer:

Option 3. 71 ft. is the distance between B and top of the hill.

Step-by-step explanation:

Let the height of the hill is h ft and the distance of A from the hill be x ft and distance from B to hill is y.

It is given distance between A and B is 45 ft. ∠BAO = 65° and ∠ABO = 80°.

We have to find the distance of B from the top of the hill.

Now from ΔACO $tan 65 = \frac{h}{45-x} = 2.14$

$h=2.14(45-x)$

From ΔBCO $tan80 = \frac{h}{x} = 5.67$

h = 5.67x

Now h = 5.67x = 2.14(45-x)

5.67x = 96.3 - 2.14x

2.14x + 5.67x = 96.3

7.81x = 96.3

x = 96.3/7.81 = 12.33 ft

Therefore $cos80 = \frac{x}{OB}$

$0.174 = \frac{12.33}{OB}$

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Therefore 71 ft is the distance between B and the top of the hill.

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3 years ago

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Answer:

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Step-by-step explanation:

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