Question

Two triangles are formed by the four lines described below. Both triangles share lines a and b. A side of one triangle is contained in line c, and a side of the other triangle is contained in line d. How can you use this information to determine whether the triangles are congruent?
Line a: y=3x+2
Line b: y=-1/3x-1
Line c: passes through points (1,5) and (3,-2)
Line d: passes through points (-6,1) and (-3,-7)

Answer 1

The lengths of sides are equal, hence the triangle formed are congruent.

Step-by-step explanation:

With the given information we need to draw the graph first

draw x axis and y axis

a: y=3x+2

b: y=-1/3x-1

c: passes through points (1,5) and (3,-2)

d: passes through points (-6,1) and (-3,-7)

Using the points given draw the four lines and mark the points

we have four lines namely a,b,c,d

we have Δ AOB and Δ COD

AB = $\sqrt{(3-1)^2 +(-2-5)^2}$

= $\sqrt{53}$

CD = $\sqrt{(-6+3)^2 +(1+7)^2}$

= $\sqrt{75}$

equation of BD = x+3y +3 =0

equation of AC = y=3x+2

therefore coordinates of 0 ≡ ($\frac{-3}{10}$,$\frac{-7}{10}$ )

OD = 1.7 $\sqrt{10}$                    OC = 2.1 $\sqrt{10}$

OB = 1.3 $\sqrt{10}$                    OA = 1.9 $\sqrt{10}$

None of the corresponding lengths of sides are equal. hence the triangle formed are congruent.