Fill in the blanks to make the statements true.In the given figure, AB

1.	Fill in the blanks to make the statements true.In the given figure, AB = AD and ∠BAC = ∠DAC. Then(i) ∆ ________ ≅ AABC.(ii) BC = ________(iii) ∠BCA = ________(iv) Line segment AC bisects ________ and ________
Answer» In ∆ABC and ∆ADC, AC = AC [common] ∠BAC = ∠DAC [given] AB = AD [given] ∴ ∆ABC ≅ ∆ADC [SAS criterion] ∴ BC = DC [By C.P.C.T.] and ∠BCA = ∠DCA [By C.P.C.T.] (i) ∆ADC ≅ ∆ABC (ii) BC = DC (iii) ∠BCA = ∠DCA (iv) Line segment AC bisects ∠BAD and ∠BCD.

Fill in the blanks to make the statements true.In the given figure, AB = AD and ∠BAC = ∠DAC. Then(i) ∆ ≅ AABC.(ii) BC = (iii) ∠BCA = (iv) Line segment AC bisects and

Answer»

In ∆ABC and ∆ADC,

AC = AC [common]

∠BAC = ∠DAC [given]

AB = AD [given]

∴ ∆ABC ≅ ∆ADC [SAS criterion]

∴ BC = DC [By C.P.C.T.]

and ∠BCA = ∠DCA [By C.P.C.T.]

(i) ∆ADC ≅ ∆ABC

(ii) BC = DC

(iii) ∠BCA = ∠DCA

(iv) Line segment AC bisects ∠BAD and ∠BCD.