Verified Diagonal AC divides the parallelogram into two triangles $\vartriangle $ABC and $\vartriangle $ADC.In $\vartriangle $ABC and $\vartriangle $ADC:$\because $ AD||BC$\angle $BAC = $\angle $DCA ( By alternate angle)AC = AC (Common side)$\angle $BCA = $\angle $DAC ( By alternate angle)In these two triangles, one side and two angles made on this side are equal.Therefore by ASA rule of congruence: $\vartriangle $ABC $ \cong $ $\vartriangle $ADC.Since, both these triangles are congruent. So, all the corresponding sides and angles of one triangle are equal to that of the other.$\therefore $ AD= BC And AB = CD.Therefore, it is proved that the diagonal of a parallelogram divides it into two congruent triangles and also opposite sides of a parallelogram are equal.Note- In the question where you have to show two triangles congruent. You should remember the following rule of congruence:1.SSS (All corresponding sides of one triangle is equal to other triangle)2.SAS (Two sides and one angle between the two sides of one triangle is equal to the other)3. ASA (one side and two angles made on this side are equal)4.RHS ( This is for right triangles. One side and hypotenuse of one right triangle is equal to other right triangle) Read Less Book your Free Demo session > Solution The correct option is A True Suppose ABCD is a parallelogram and BD is the diagonal. There are two triangles - Δ ABD and Δ CDB In Δ ABD and Δ CDB, AD = BC (opposite sides of a parallelogram are equal) AB = CD (opposite sides of a parallelogram are equal) BD is common ∴ By SSS criterion of congruency, Δ ABD ≅ Δ CDB Hence, the given statement is true. Suggest Corrections 6 > Solution The correct option is A True In parallelogram ABCD, diagonal BD divides it into 2 equal triangle. Since ABCD is a parallelogram, the opposite sides are equal. Therefore, AB = CD and AD = BC. In triangles ABD and CBD AB = CD (Opposite sides of a parallelogram) AD = BC (Opposite sides of a parallelogram) BD = BD ( common) Thus, by SSS congruency condition. △ ABD ≅ △ CBD. Therefore, we can say that the diagonal of a parallelogram divides it into 2 congruent triangles. Hence, option (A) is correct. Suggest Corrections 24 |