Question

Triangle JKL has vertices J(2,5), K(1,1), and L(5,2). Triangle QNP has vertices Q(-4,4), N(-3,0), and P(-7,1). Is (triangle)JKL congruent to (triangle)QNP?

Answer 1

Yes they are

Explanation:

In the triangle JKL, the sides can be calculated as following:

• J(2;5); K(1;1)

=> JK =
`\sqrt{(1-2)^(2) + (1-5)^(2) } = \sqrt{(-1)^(2)+(-4)^(2) } = √(1+16)=√(17)`

• J(2;5); L(5;2)

=> JL =
`\sqrt{(5-2)^(2) + (2-5)^(2) } = \sqrt{3^(2)+(-3)^(2) } = √(9+9)=√(18) = 3√(2)`

• K(1;1); L(5;2)

=> KL =
`\sqrt{(5-1)^(2) + (2-1)^(2) } = \sqrt{4^(2)+1^(2) } = √(1+16)=√(17)`

In the triangle QNP, the sides can be calculate as following:

• Q(-4;4); N(-3;0)

=> QN =
`\sqrt{[-3-(-4)]^(2) + (0-4)^(2) } = \sqrt{1^(2)+(-4)^(2) } = √(1+16)=√(17)`

• Q (-4;4); P(-7;1)

=> QP =
`\sqrt{[-7-(-4)]^(2) + (1-4)^(2) } = \sqrt{(-3)^(2)+(-3)^(2) } = √(9+9)=√(18) = 3√(2)`

• N(-3;0); P(-7;1)

=> NP =
`\sqrt{[-7-(-3)]^(2) + (1-0)^(2) } = \sqrt{(-4)^(2)+1^(2) } = √(16+1)=√(17)`

It can be seen that QPN and JKL have: JK = QN; JL = QP; KL = NP

=> They are congruent triangles