When considering a term(s) inside parentheses, and there is an exponent

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.

8 0

3 years ago

Solve the following equation system by graphing X-Y=4 X+Y=2 What is the solution?

AfilCa [17]

X-Y=4,
X+Y=2
-------------add
2x = 6
x = 3

X - Y =4
3 - Y = 4
Y = 3 - 4
Y = -1

solution (3 , -1)

4 0

3 years ago

Which situation best shows causation?

dangina [55]

A cause and effect relationship exist between two variables, when one

variable event is made to happen by the other variable.

The situation which best shows causation is option B) The amount of time a

cell phone is used affects the charge of the battery.

Reasons:

Causation is the condition in which the occurrence of an event is caused by

or contributed to by another event. Such that the incident or observation

identified as the cause is responsible for the event, while the the

occurrence of the event depends on the cause being put in place.

Option A) A rectangle of a given width can have different dimensions of length

Option C) Milkshakes and ice cream bars can have different customer base, such that the number of milkshake and ice cream bars sold can be equal

Option D) The balls used in a soccer match are provided by the officials of the game

Therefore;

The situation which shows causation is B) The amount of time a cell phone is used affects the charge of the battery.

The option is correct because, a cell phone is powered by battery, and

therefore, the more the cell phone is used, the battery power is used up

and therefore, the charge on the battery is reduced.

Learn more here:

brainly.com/question/18404964

3 0

3 years ago

Can you pls put in order I need help ASAP :3 thanks if you can. I will make Brainly

Brums [2.3K]

Answer:

This might get confusing but bear with me.

The top two are correct, leave them where they are. The 6th one down is step three, the 8th one down is step four, the 3rd one down is step five, the 4th one down is step six, the 7th ne down is step seven so leave it alone, and the 5th one down is step 8.

7 0

3 years ago

17 gallons of water are used to completely fill 4 fish tanks. If each tank holds the same amount of water how many gallons will

Kay [80]

Each tank holds 4.25 gallons! 17/4 is 4.25 :) hope this helps!

6 0

3 years ago