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pychu [463]
2 years ago
9

100 POINTS!!!!

Mathematics
2 answers:
Svetllana [295]2 years ago
7 0

QUESTION:

Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by drawing line segments and . Then construct the perpendicular bisectors of and , and name the point of intersection of the perpendicular bisectors O. How do you know that point O is the center of the circle that passes through the three points?

ANSWER:

When we join all three points (D, E, F) then it forms a Δ DEF.

Now, Let the midpoint of EF be M and the midpoint of ED be N and Join point I to E, D and F.

Because, IN is both an altitude and median to Δ EID, then Δ EID is an isosceles triangle, and IE = ID.

Similarly, we see that IE = IF.

So, we can conclude that,

  • IE = ID = EF.

Hence, O is the center of the circle with radius IE, ID or EF.

NOTE: See picture attached.

weeeeeb [17]2 years ago
5 0

Answer:

O is the center of the circle with radius IE(=ID=EF)

Step-by-step explanation:

Join all 3 points D, E, F, forming the triangle DEF.

Let the midpoint of EF be M and the midpoint of ED be N. (first picture)

Join point I to E, D and F.

Since IN is both an altitude and median to triangle EID, then triangle EID is an isosceles triangle, and IE=ID

similarly, we see that IE=IF.

conclusion: IE=ID=EF.

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Four times the sum of 8 and some number is 4. What is the number?
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\Huge \boxed{\mathrm{-7}}

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Step-by-step explanation:

Let the number be x.

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x+8=1

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\rule[225]{225}{2}

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2 years ago
What other information do you need to prove ΔABE is congruent to ΔEDA by SSS?
Stels [109]

To prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.

What is an equilateral triangle?

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Here, we have

AEC is a triangle in which B∈ AC and D∈ EC

Such that,

∠ABE = 90°,

∠ADE = 90°,

Also, BC = CD

Now, we have to prove that :

Δ ABE is congruent to Δ EDA

Proof :

If EAC is an equilateral triangle,

By the property of an equilateral triangle,

EA = AC = EC

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AB + BC = ED + CD

AB + CD = ED + CD

AB = ED

Also, AE = AE ( common segment )

Now, if in two right triangles hypotenuse are equal and any corresponding legs are equal,

Then, the other legs must be equal,

That is, BE = DA,

Hence, by the SSS postulate of congruence,

Δ ABE ≅ Δ EDA

Hence, to prove ΔABE is congruent to ΔEDA by SSS we need that EAC should be an equilateral triangle.

To learn more about the equilateral triangle from the given link

brainly.com/question/15294703

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