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
>
A diagonal of a parallelogram divides it into two congruent triangles.
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
>
The diagonal of a parallelogram divides it into 2 congruent triangles. State whether true or false.
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