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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.

8 0

2 years ago

04.04 match the term with the definition

MA_775_DIABLO [31]

i need the terms and definitions to answer this-

6 0

2 years ago

Department stores are about to release a new makeup line, and a promotional kit will be sold for $42.75. The cost to produce the

ohaa [14]

Answer: 569

Step-by-step explanation:

5 0

2 years ago

X. Y

Dovator [93]

Answer:

Slope: 5

Y-intercept: 0

Equation: y=5x

Step-by-step explanation:

Lets look for an equation of the format y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).

Slope is defined as the "Rise/Run" of the line. The change in y(the rise) for a change in x(the run). This can be calculated by taking any two of the given data points. I'll pick (1,5) and (5,25):

Rise = (25 - 5) = 20

Run = (5 - 1) = 4

The Rise/Run, or slope, m, is (20/4) or 5.

The equation becomes y = 5x + b.

To find b, the y-intercept, enter any of the points into the equation and solve for b:

y = 5x + b

y = 5x + b for (4,20)

20 = 5*(4) + b

b = 0

The line goes through the origin at x = 0 (0,0).

The equation is y = 5x + 0 or just y = 5x.

Slope: 5

Y-intercept: 0

Equation: y=5x

4 0

1 year ago

9th question help ?!

Daniel [21]

Hey there! :)

You have to find the area of all of them and add it together.

Formulas:

Area of a square: l · w
Area of a triangle: (b · h) ÷ 2

Square -

l = 3
w = 3

3 × 3 = 9

Triangle -

b = 3
h = 3

(3 × 3) ÷ 2
9 ÷ 2 = 4.5

There are 4 triangles

4.5 × 4 = 18

9 + 18 = 27

The surface area ⇒ 27 cm²

5 0

3 years ago