Question

ABC and DBC are two isosceles triangles on the same base BC (see Fig. 3.5). Show that ABD = ZACD.​

Answer 1

Given:-

Two triangles

ABC and DBC on the same base BC

To prove :-

Angle ABD = Angle ACD

Construction :-

Join AD

Proff :-

In traingles ABC and ABD

AB = AC [ As ABC is a Isosceles triangle ]

BC = DC [ As BDC is Isosceles triangle ]

AD = AD [ Common ]

Therefore SSS Congrency rule

$\: \: \sf\bold{\pink{ \: Triangle \: ABD ≅ \: Triangle \: ACD \: \: }}$

∴ Angle B = Angle C [ C.P.C.T ]

$∴ \: \: \: \sf\bold{\red{Angle \: ABD \: = Angle \: ACD \: \: }}$

Hence proved

Formula used :-

SSS (Side-Side-Side) =

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

Note :-

Figure in attachment