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Triangle ABC has vertices A(2,0), B(6,0) and C(4,5). Prove that the triangle is isosceles and ​not​ a right triangle

1 Answer

2 votes

Answer:

Step-by-step explanation:

An isosceles triangle is one with two equal lengths.

To find the lengths of the sides with coordinates

(

x

1

,

y

1

)

,

(

x

2

,

y

2

)

we use Pythagoras' theorem

d

=

(

x

2

x

2

)

2

+

(

y

2

y

1

)

2

from the information given

d

1

=

(

13

9

)

2

+

(

2

8

)

2

d

1

=

4

2

+

6

2

=

52

(

1

)

d

2

=

(

13

5

)

2

+

(

2

2

)

2

d

2

=

8

2

+

0

2

=

64

=

8

(

2

)

d

3

=

(

9

5

)

2

+

(

8

2

)

2

d

3

=

4

2

+

6

2

=

52

(

3

)

we see

d

1

=

d

3Explanation:

An isosceles triangle is one with two equal lengths.

To find the lengths of the sides with coordinates

(

x

1

,

y

1

)

,

(

x

2

,

y

2

)

we use Pythagoras' theorem

d

=

(

x

2

x

2

)

2

+

(

y

2

y

1

)

2

from the information given

d

1

=

(

13

9

)

2

+

(

2

8

)

2

d

1

=

4

2

+

6

2

=

52

(

1

)

d

2

=

(

13

5

)

2

+

(

2

2

)

2

d

2

=

8

2

+

0

2

=

64

=

8

(

2

)

d

3

=

(

9

5

)

2

+

(

8

2

)

2

d

3

=

4

2

+

6

2

=

52

(

3

)

we see

d

1

=

d

3Explanation:

An isosceles triangle is one with two equal lengths.

To find the lengths of the sides with coordinates

(

x

1

,

y

1

)

,

(

x

2

,

y

2

)

we use Pythagoras' theorem

d

=

(

x

2

x

2

)

2

+

(

y

2

y

1

)

2

from the information given

d

1

=

(

13

9

)

2

+

(

2

8

)

2

d

1

=

4

2

+

6

2

=

52

(

1

)

d

2

=

(

13

5

)

2

+

(

2

2

)

2

d

2

=

8

2

+

0

2

=

64

=

8

(

2

)

d

3

=

(

9

5

)

2

+

(

8

2

)

2

d

3

=

4

2

+

6

2

=

52

(

3

)

we see

d

1

=

d

3

User Ehsan Sajjad
by
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