Which is bigger 1 2/9or 1.2

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

(2x - 3y)(4x - y) Please help

andre [41]

(2x - 3y) (4x - y) = 8x² - 2xy - 12xy + 3y²

(2x - 3y) (4x - y) = 8x² -14xy + 3y²

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Answer:8x² -14xy + 3y²
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3 0

2 years ago

Pentagon DEFGH is translated 4 units to the right to create pentagon UVXYZ. DE is 5 cm long. What is the length of UV?

Wewaii [24]

Without seeing the picture, we don't know how DE and UV are related.

3 0

3 years ago

A news service conducted a survey of 1026 adults ages 18 years or older in a certain country, August 31minus−September 2, 2015

Musya8 [376]

Answer:

B. To determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar.

Step-by-step explanation:

Given that:

sample size = 1026

sample proportion = 0.36

Margin of error = 55% = 0.55

Confidence interval level = 99%

The purpose of this question is to determine the research objective:

The research objectives indicate the intention of the study, the objectives,\ or the main idea. This main idea arises from a need (the research problem) and refined into specific questions (i.e. the research questions). From, the given information, the research objective is to determine the percent of adults in the country who believe the federal government wastes 51 cents or more of every dollar.

7 0

2 years ago

Carmen works at a pet store. To feed 8 cats, she empties four 6-once cans of cat food into a large bowl. Carmen divides the food

Ipatiy [6.2K]

4 x 6 ounces = 24 ounces (total)
24 ounces ÷ 8 = 3 ounces

Ans : 3 ounces

5 0

3 years ago

Which is bigger 1 2/9￼or 1.2

Which is bigger 1 2/9or 1.2