Question

Find the values of x and y using the information shown in figure 3.37. Find the measure of ∠ABD and m∠ACD.

Answer 1

Given ,

∆ABC and ∆DBC are two isosceles

triangles on the same base BC.

Join A to D .

Now ,

In ∆DBA and ∆DCA

BD = DC ( S )

BA = CA ( S )

DA common side .[ construction ]

Therefore ,

∆DBA is congruent to ∆DCA .

[ SSS congruence Rule ]

<ABD = <ACD [ CPCT ]

x + 60° = 50° + y

Therefore ,

x = 50° ,

y = 60°

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