Question

Observe the figure and state the three pairs of equal parts in triangles ABC and DCB. (i) Is ΔABC = ΔDCB? Why? (ii) Is AB = DC? Why? (iii) Is AC = DB? Why?

Answer 1

Answer:-

Formula Used/Theory:-

→ When two angles and side between both the angles are equal in both the triangles then triangles are congruent by ASA congruence criterion

In ∆ABC and ∆DCB

∠B = ∠C (Both 70° )

∠ACB = ∠DCB (Both 30° )

BC = BC (common)

∆ABC ≅ ∆DCB

⇒ Hence; both triangles are congruent by ASA congruence

If ∆ABC ≅ ∆DCB then;

If triangles are congruent then all 3 sides of triangle are equal to all 3 sides of other triangle

BC = BC

⇒ AB = DC

⇒ AC = DB