Draw a triangle ABC with side BC = 6 cm, AB=5 cm and ∠ABC=60°. Then construct a triangle whose sides are of the corresponding sides of the triangle ABC.

Question

Draw a triangle ABC with side BC = 6 cm, AB=5 cm and ∠ ABC=60°. Then construct a triangle whose sides are of the corresponding sides of the triangle ABC.

Philoid · Accepted Answer

△A′BC′ whose sides of the corresponding sides of can be drawn as follows.

Step 1 Draw a △ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = .

Step 2 Draw a ray BX making an acute angle with BC on the opposite side of vertex A.

Step 3 Locate 4 points (as 4 is greater in 3 and 4), B1,B2,B3,B4 on line segment BX.

Step 4 Join B4C and draw a line through B3 , parallel to B4C intersecting BC at C′

Step 5 Draw a line through C' parallel to AC intersecting AB at A'.△A′BC′ is the required triangle.

Justification

∠A=60° (Common)

∠C=∠C'

By AA similarity condition

Also,

AB’=AB ,B’C’=BC and AC’=AC