Answer:
m∠DEF = 90°
Step-by-step explanation:
As we know to determine the angle between two lines with the given equations or vertices we use the formula
[tex]tan\theta =\frac{m_{2}-m_{1}}{1+m_{2}m_{1}}[/tex]
Now we have been given the vertices of a triangle as D(5, 7) E(4, 3) F(8, 2)
To measure m∠ DEF will use the formula
Since slope of DE [tex]m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m_{1}=\frac{7-3}{5-4}=\frac{4}{1}=4[/tex]
Slope of EF [tex]m_{2}=\frac{3-2}{4-8}=\frac{1}{-4}=-\frac{1}{4}[/tex]
Now m∠DEF = [tex]tan\theta = \frac{\frac{17}{4}}{1-1}=\infty[/tex]
Therefore [tex]\theta =90[/tex]
Answer is ∠DEF = 90°
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)
To find side DE
D(5,7) E (4,3)
DE = √[(5-4)² + (7 - 3)²] = √17
To find side EF
E (4,3) ,F(8,2)
EF = √[(8-4)² + (2 - 3)²] = √17
To find side DF
D(5,7) ,F(8,2)
EF = √[(8-5)² + (2 - 7)²] = √34 = √2√17
To find the ratio of sides
The sides are in the ratio
DE : EF : DF = √17 : √17 : √2√17 = 1 : 1 : √2
To find the angle DEF
The sides are in the ratio 1 : 1 : √2
Therefore triangle DEF is a right angled triangle.
DE = EF
<DEF = 90°
