Question

In the figure AB &CD are the lines 2x-y+6=0 & x-2y=4.
i)Write the coordinates of A, B, C, D
ii) Prove that triangle OAB is congruent to triangle ODC
Please solve the second question​

Answer 1

Given:  AB &CD are the lines 2x - y + 6 = 0 & x - 2y = 4.

To find: Prove that triangle OAB is congruent to triangle ODC.

Solution:

• Now we have given the points in figure as:

             A(0,6) , B(-3,0) , C(0,-2) and D(4,0)

• The triangles cannot be congruent because :

             CB = √13 and DA = 2√13

             CB ≠ AD

             AC ≠ BD

So the triangles cannot be congruent.

• Consider triangle OAB and triangle ODC, we have:

             OB = 3 cm, OA = 6 cm, OC = 2 cm and OD = 4 cm.

• Now:

             OA/OD = 6/4 = 3/2

             angle AOB = angle DOC ..........(vertically opposite angles

             OB/OC = 3/2

             So OA/OD = OB/OC = 3/2

• So by SAS criteria, we have:

• triangle OAB is similar to triangle ODC

Answer:

            So the triangles are not congruent but similar.