08.12.2022

Given a triangle with the following points determine if the triangle is scalene isosceles or equilateral

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Mathematics

Correct answer gets brainliest Given the vertices A(2,-2) B(0,4) and C(-4,-4): Classify the triangle by its sides: scalene, isosceles, or equilateral (Is the triangle scalene, isosceles, or equilateral?) Classify the triangle by its angles: acute, obtuse, or right (Is the triangle acute, obtuse, or right?)

Step-by-step answer

P Answered by PhD

sides: isoscelesangles: right

Step-by-step explanation:

At first, lets find the distance from one point to the other.

$d(A,B)=\sqrt{(x_{A}-x_{B} )^2 +(y_{A}-y_{B} )^2 } \\d(A,B)=\sqrt{(2-0 )^2 +(-2-4 )^2 } \\d(A,B)=\sqrt{4 +36 } = \sqrt{40 } = \sqrt{4 * 10 } = 2\sqrt{10}$

The same way, you can find that:

$d(A,C)= 2\sqrt{10}\\d(A,B)= 2\sqrt{20}$

Since the triangle has only its two sides equal to each other (AB = AC),

it's an isosceles one.

As long as the angles are concerned, we gotta "cheat". In other words, we see that:

$AB^2 + AC^2 = (\sqrt{40})^2 + (\sqrt{40})^2 = 40 + 40 = 80\\ AB^2 + AC^2 = 80 = (2\sqrt{20})^2 = BC^2\\AB^2 + AC^2 = BC^2$

By the inverse of pythagorean theorem, we know that if the above equation holds, then we have a right-angled triangle. That is to say that,

A = 90

Since its an isosceles triangle, AB = AC,

B = C = (180 - A)/2 = 45 degrees

Correct answer gets brainliestGiven the vertices A(2,-2) B(0,4) and C(-4,-4): Classify the triangle

Mathematics

Step-by-step answer

P Answered by PhD

sides: isoscelesangles: right

Step-by-step explanation:

At first, lets find the distance from one point to the other.

$d(A,B)=\sqrt{(x_{A}-x_{B} )^2 +(y_{A}-y_{B} )^2 } \\d(A,B)=\sqrt{(2-0 )^2 +(-2-4 )^2 } \\d(A,B)=\sqrt{4 +36 } = \sqrt{40 } = \sqrt{4 * 10 } = 2\sqrt{10}$

The same way, you can find that:

$d(A,C)= 2\sqrt{10}\\d(A,B)= 2\sqrt{20}$

Since the triangle has only its two sides equal to each other (AB = AC),

it's an isosceles one.

As long as the angles are concerned, we gotta "cheat". In other words, we see that:

$AB^2 + AC^2 = (\sqrt{40})^2 + (\sqrt{40})^2 = 40 + 40 = 80\\ AB^2 + AC^2 = 80 = (2\sqrt{20})^2 = BC^2\\AB^2 + AC^2 = BC^2$

By the inverse of pythagorean theorem, we know that if the above equation holds, then we have a right-angled triangle. That is to say that,

A = 90

Since its an isosceles triangle, AB = AC,

B = C = (180 - A)/2 = 45 degrees

Mathematics

Given below are the coordinates of the vertices of a triangle. find the lengths of the sides of the triangle, then click to identify the triangle as scalene, isosceles, or equilateral. w(5, -5), x(-2, -2), y(8, 2) isosclese scalene equilateral

Step-by-step answer

P Answered by Master

After plotting the points and connecting them you will get an isosceles triangle
Given below are the coordinates of the vertices of a triangle. find the lengths of the sides of the

Mathematics

Given below are the coordinates of the vertices of a triangle. find the lengths of the sides of the triangle, then identify if the triangle is scalene, isosceles, or equilateral. w(5, -5), x(-2, -2), y(8, 2)

Step-by-step answer

P Answered by Master

I believe this is an isosceles triangle

Mathematics

Given below are the coordinates of the vertices of a triangle. Find the lengths of the sides of the triangle, then click to identify the triangle as scalene, isosceles, or equilateral. W(5, -5), X(-2, -2), Y(8, 2)

Step-by-step answer

P Answered by Master

The triangle would be isosceles.

Step-by-step explanation:

hope this helps~

Mathematics

Step-by-step answer

P Answered by Master

ΔPQR is an equilateral triangle.

Step-by-step explanation: The vertices of a triangle PQR are given as follows:

P(0, 0), Q(6, 0) and R(3, 3√3).

We are to find the type of the triangle by finding the lengths of its three sides.

The lengths of the three sides PQ, QR and PR are calculated using distance formula as follows:

$PQ=\sqrt{(6-0)^2+(0-0)^2}=\sqrt{36+0}=\sqrt{36}=6,\\\\QR=\sqrt{(3-6)^2+(3\sqrt3-0)^2}=\sqrt{9+27}=\sqrt{36}=6,\\\\PR=\sqrt{(0-3)^2+(0-3\sqrt3)^2}=\sqrt{9+27}=\sqrt{36}=6.$

Therefore, PQ = QR = PR.

All the sides of the triangle PQR are equal, and so the triangle is equilateral.

Thus, ΔPQR is an equilateral triangle.

Mathematics

Step-by-step answer

P Answered by Specialist

The length of a segment, given the extremities, is:
√[(x₂ - x₁)² + (y₂ - y₁)²]

Therefore:

RS = √[(3-1)² + (1-3)²] = √(4+4) = √8

RT = √[(5-1)² + (2-3)²] = √(16+1) = √17

ST = √[(5-3)² + (2-1)²] = √(4+1) = √5

Since the lengths are all different, the triangle is scalene.

Mathematics

Step-by-step answer

P Answered by Specialist

To find the length of the sides, we use the Pythagorean Theorem. First, let's look at the side RS. R is at (1,3), and S is at (3,1). Therefore, to find RS, we use the difference in height and length: $a = \sqrt{ {b}^{2} + {c}^{2} } \\ a = \sqrt{ {(3 - 1)}^{2} + {(1 - 3)}^{2} } \\ a = \sqrt{ {(2)}^{2} + {( - 2)}^{2} } \\ a = \sqrt{4 + 4} \\ a = \sqrt{8}$
The length of side RS is square root 8.

Side ST is made from point S (3,1) and point T (5,2).
$a = \sqrt{ {(5 - 3)}^{2} + {(2 - 1)}^{2} } \\ a = \sqrt{ {(2)}^{2} + {(1)}^{2} } \\ a = \sqrt{4 + 1} \\ a = \sqrt{5}$
The length of side ST is root 5.

Side RT is between R (1,3) and T (5,2).
$a = \sqrt{ {(1 - 5)}^{2} + {(3 - 2)}^{2} } \\ a = \sqrt{ {( - 4)}^{2} + {(1)}^{2} } \\ a = \sqrt{16 + 1} \\ a = \sqrt{17}$
The side RT is root 17. The triangle is scalene, meaning it has three sides of different lengths.
Given below are the coordinates of the vertices of a triangle. find the lengths of the sides of the

Mathematics

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

KL = $\sqrt{(3-7)^2 +(4-0)^2}$ = 4√2

LM = $\sqrt{(2-3)^2 +(-1-4)^2}$ = √26

KM = $\sqrt{(2-7)^2 +(-1-0)^2}$ = √26

ΔKLM is isosceles.

Mathematics

Select all the ways you can describe the given polygon. regular irregular scalene isosceles equilateral acute right obtuse equiangular

Step-by-step answer

P Answered by PhD

>regular triangle, we call equilateral triangles regular polygons.

>isosceles, as an equilaterial triangle is a specific type of isosceles due to more than one side being of equal length and angle.

>equilateral, where all sides and angles are the same.

>acute, as all 3 angles are less than 90

>equiangular. equilateral triangles are also described as equiangular.

Step-by-step explanation:

Just the five ways above can describe the polygon shown, as the angles of a scalene triangle are unequal. as are their sides, equilaterial have same sides and angles. Obtuse have angles larger than 90deg less than 180 deg.

Whilst irregular are triangles and shapes that have uneven sides and are not right or isosceles.

Right triangles have one angle that is exactly 90 deg.

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