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3 years ago

In the figure below, segment CD is parallel to segment EF and point H bisects segment DE :

Mathematics

1 answer:

Grace [21]3 years ago

4 0

Answer:

See explanation

Step-by-step explanation:

In the figure below, segment CD is parallel to segment EF, DE is a transversal, then angles DIH and HGI are congruent as alternate interior angles when two parallel lines are cut by a transversal.

Consider triangles DIH and EGH. In these triangles,

$\angle DIH\cong \angle EGH$ as alternate interior angles;
$\angle DHI\cong \angle GHE$ as vertical angles;
$DH\cong HE$ because point H bisects segment DE (given).

Thus,

$\triangle DIH\cong \triangle EGH$ by AAS postulate

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Answer:

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2 years ago

20 points and Brainliest !

soldier1979 [14.2K]

Answer:

y = -5/6x + 6

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2 years ago

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James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements ar

GaryK [48]

Answer:

The expressions 7x + 4 and 3x + 5 + 4x = 1 are equivalent for every value of x.

Step-by-step explanation:

Expressions - 7x + 4 and 3x + 5 + 4x = 1.

1. When x = 2, both expressions have a value of 18. Let's find out:

1st expression : 7(2) + 4 = 14+4 = 18

2nd expression : 3(2) + 5 + 4(2) = 1

or 6 + 5 + 8 - 1 = 18

Values of both the expressions is 18, hence it is correct statement.

2.The expressions are only equivalent for x = 4 and x = 6.

This is incorrect statement as we just calculated above that the expressions are equivalent for x = 2. Hence, it is incorrect.

3. The expressions have equivalent values for any value of x.

Say, x = 0, then,

7x + 4 = 7 (0) + 4 = 4 and,

3x + 5 + 4x - 1 = 3(0) + 5 + 4(0) - 1 = 5-1 = 4

The statement holds.

Let's try again for x = 12,

7x + 4 = 7(12) + 4 = 88 and,

3x + 5 + 4x - 1 = 3(12) + 5 + 4(12) - 1 = 36 + 5 + 48 -1 = 88

Let's try again for x = 13,

7x + 4 = 7(13) + 4 = 95 and,

3x + 5 + 4x - 1 = 3(13) + 5 + 4(13) - 1 = 39 + 5 + 52 -1 = 95

Clearly, it holds for every value of x, whether it is odd or even. Hence, it is correct statement.

_______________________________________________________

Trick: 7x + 4 = 0....(1) and,

3x + 5 + 4x = 1

Rearranging the terms of above expression, we get,

(3x + 4x) + (5 - 1) =0

or 7x + 4 = 0...(2)

clearly both (1) & (2) are equivalent.

_____________________________________________________

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2 years ago

Square: Area 25 units2.<br> What is the square root?

stealth61 [152]

Answer:

The square root is 5 units.

Step-by-step explanation:

It is given that:

Square area is 25 units square.

We have to find the square root.

Square root = $\sqrt{25}$

Square root = $\sqrt{5*5}$

Square root = 5 units

Therefore,

The square root is 5 units.

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