Mathematics, 01.08.2019 21:40 sierralynnbaldp16d4b

Match each set of vertices with the type of triangle they form. tiles a(2, 0), b(3, 2), c(5, 1) obtuse scalene triangle a(4, 2), b(6, 2), c(5, 3.73) isosceles right triangle a(-5, 2), b(-4, 4), c(-2, 2) right triangle a(-3, 1), b(-3, 4), c(-1, 1) acute scalene triangle a(-4, 2), b(-2, 4), c(-1, 4)

Answers: 2

Show answers

Answers

Answer from: reaperqueen21

The correct match is given below.

Step-by-step explanation: We know that the type of angled triangle can be found out by the following method:

if sum of the squares of two sides of shortest lengths > Square of length the greatest side ⇒ it is an acute angled triangle

if sum of the squares of two sides of shortest lengths = Square of length the greatest side ⇒ it is a right angled triangle

if sum of the squares of two sides of shortest lengths < Square of length the greatest side ⇒ it is an obtuse angled-triangle.

Also, if all the sides of the triangle are equal in length, then the triangle is equilateral.

if two sides of the triangle are equal in length, then the triangle is isosceles.

if none of the sides of the triangle are equal in length, then the triangle is scalene.

For the first trianlge: A(2, 0), B(3, 2), C(5, 1).

We have

$AB=\sqrt{(3-2)^2+(2-0)^2}=\sqrt{1+4}=\sqrt{5},\\\\BC=\sqrt{(5-3)^2+(1-2)^2}=\sqrt{4+1}=\sqrt{5},\\\\CA=\sqrt{(2-5)^2+(0-1)^2}=\sqrt{10}.$

Since AB = BC and AB² + BC² = CA², so the triangle is isosceles right-angled triangle.

For the second trianlge: A(4, 2), B(6, 2), C(5, 3.73).

We have

$AB=\sqrt{(6-4)^2+(2-2)^2}=\sqrt{4+0}=2,\\\\BC=\sqrt{(5-6)^2+(2-3.73)^2}=\sqrt{1+2.99}=\sqrt{3.99},\\\\CA=\sqrt{(4-5)^2+(2-3.73)^2}=\sqrt{3.99}.$

Since BC = CA and BC² + CA² > CA², so the triangle is isosceles acute angled triangle.

For the third trianlge: A(-5, 2), B(-4, 4), C(-2, 2).

We have

$AB=\sqrt{(-4+5)^2+(4-2)^2}=\sqrt{1+4}=\sqrt{5},\\\\BC=\sqrt{(-2+4)^2+(2-4)^2}=\sqrt{4+4}=2\sqrt{2},\\\\CA=\sqrt{(-5+2)^2+(2-2)^2}=\sqrt{9}=3.$

Since AB ≠ BC ≠ CA and AB² + BC² > CA², so the triangle is acute scalene triangle.

For the fourth trianlge: A(-3, 1), B(-3, 4), C(-1, 1).

We have

$AB=\sqrt{(-3+3)^2+(4-1)^2}=3,\\\\BC=\sqrt{(-1+3)^2+(1-4)^2}=\sqrt{4+9}=\sqrt{13},\\\\CA=\sqrt{(-3+1)^2+(1-1)^2}=\sqrt{4}=2.$

Since AB ≠ BC ≠ CA and BC² + CA² = AB², so the triangle is scalene right-angled triangle.

For the fifth trianlge: A(-4, 2), B(-2, 4), C(-1, 4).

We have

$AB=\sqrt{(-2+4)^2+(4-2)^2}=2\sqrt2,\\\\BC=\sqrt{(-1+2)^2+(4-4)^2}=\sqrt{1+0}=1,\\\\CA=\sqrt{(-4+1)^2+(2-4)^2}=\sqrt{9+4}=\sqrt{13}.$

Since AB ≠ BC ≠ CA and AB² + BC² < AB², so the triangle is scalene obtuse-angled triangle.

Thus, the correct match is

A(2, 0), B(3, 2), C(5, 1) isosceles right-angled triangle.

A(4, 2), B(6, 2), C(5, 3.73) isosceles acute angled triangle.

A(-5, 2), B(-4, 4), C(-2, 2) acute scalene triangle.

A(-3, 1), B(-3, 4), C(-1, 1) scalene right-angled triangle.

A(-4, 2), B(-2, 4), C(-1, 4) scalene obtuse-angled triangle.

Answer from: Quest

343t464564435rri76i6u

step-by-step explanation:

because i said it is

Answer from: Quest

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 17:00

What is the difference between the points (4, 7) and (4, -5)? a. 0 units b. 2 units c. 4 units d. 12 units

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

Solve this problem! extra ! 3025/5.5 = a/90.75

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Look at triangle wxy what is the length (in centimeters) of the side wy of the triangle?

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Questions 7-8. use the following table to answer. year 2006 2007 2008 2009 2010 2011 2012 2013 cpi 201.6 207.342 215.303 214.537 218.056 224.939 229.594 232.957 7. suppose you bought a house in 2006 for $120,000. use the table above to calculate the 2013 value adjusted for inflation. (round to the nearest whole number) 8. suppose you bought a house in 2013 for $90,000. use the table above to calculate the 2006 value adjusted for inflation. (round to the nearest whole number)

Answers: 3

Answer

You know the right answer?

Match each set of vertices with the type of triangle they form. tiles a(2, 0), b(3, 2), c(5, 1) obtu...

Questions

Mathematics, 28.01.2021 18:10

The cost of a council tax bill increased by 5%. The council tax bill increased by £62. Work out the cost of the council tax bill before the increase...