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3 years ago

25 Pts + Brainliest for the first correct answer.

Mathematics

1 answer:

NeTakaya3 years ago

8 0

6.)Corresponding

7.)Alternate Interior

8.)Vertical

9.)Alternate Exterior

10.)Adjacent

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Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

It can be clearly seen that:

$\angle DFE = \angle E =90-\dfrac{y}{2}$

The two angles of $\triangle EDF$ are equal hence $\triangle EDF$ is isosceles.

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3 years ago

William's typical running speed is 6 mi/h. The difference between his fastest speed and his typical speed is 1.5 min. The equati

Over [174]

Answer:

D) 7.5 mi/h. hcbhcvu yc yv. y yv yh

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2 years ago

Read 2 more answers

HELP IM DESPRITE

scZoUnD [109]

Answer:

Step-by-step explanation:

45.5 + 15.5x < 175

15.5x < 129.5

x < 8.35

Answer: 8

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2 years ago

Mary has used 160 tiles to cover 40% of the back splash in her kitchen how many tiles will it take to cover the entire back spla

dangina [55]

Answer:

400 tiles :)

Step-by-step explanation:

2/5 = 160/x

1/5 = 80/x

80 *5 = 400

6 0

3 years ago

A bag contains white marbles and red marbles, 90 in total. The number of white marbles is 6 less than 5 times the number of red

Gelneren [198K]

Answer:

W = 72

Step by step explanation:

White = W

Red = R

W + R = 90

Write an equation

W = 5R - 6

Substitute

5R - 6 = 90

Add 6 to both sides of the equation

5R = 90

Simplify

90 ÷ 5 = 18

R = 18

90 - 18 = W

W = 72

Hope this was useful to you!

8 0

3 years ago