Answer:
m<DEF = 90°
Step-by-step explanation:
It is given that, D, E and F are the vertices of a triangle.
D(5,7) E (4,3) and f(8,2)
<u>To find side DE</u>
D(5,7) E (4,3)
DE = √[(5-4)² + (7 - 3)²] = √17
<u>To find side EF</u>
E (4,3) ,F(8,2)
EF = √[(8-4)² + (2 - 3)²] = √17
<u>To find side DF</u>
D(5,7) ,F(8,2)
EF = √[(8-5)² + (2 - 7)²] = √34 = √2√17
<u>To find the ratio of sides</u>
The sides are in the ratio
DE : EF : DF = √17 : √17 : √2√17 = 1 : 1 : √2
<u>To find the angle DEF</u>
The sides are in the ratio 1 : 1 : √2
Therefore triangle DEF is a right angled triangle.
DE = EF
<DEF = 90°