Chhattisgarh Board Solutions for Exercise 3: Exercise

See the triangle pair and state which condition of congruence applies on the pair.

See the triangle pair and state which condition of congruence applies on the pair.

See the triangle pair and state which condition of congruence applies on the pair.

If $△\mathrm{ABC}\cong △\mathrm{PQR},\mathrm{AC}=3x+2,\mathrm{PR}=6x-13$ and $\mathrm{BC}=5x$ then find the value of $QR$.

With the help of the given points, find the distance between $\mathrm{A}$ and $\mathrm{B}$, also give reason to your statement.

For a running competition there is a special arrangement made for two teams. One team runs from $\mathrm{A}$ to $\mathrm{B}$ and then from $\mathrm{B}$ to $\mathrm{C}$ and returns to the starting point $\mathrm{A}$. While the other team starts from $\mathrm{C}$ and via $\mathrm{D}$ to $\mathrm{B}$ and then $\mathrm{B}$ to the point $\mathrm{C}$ again. If $\overrightarrow{\mathrm{AB}}\Vert \overrightarrow{\mathrm{CD}}$ and $\angle \mathrm{A}=\angle \mathrm{D}=90°$, then the length of the travel done by the teams are equal. Also explain your answer.

$l$ and $m$ are parallel lines, which have been intersected by the parallel lines $p$ and $q$. Show $△ABC\cong △CDA$.

In a figure $AC=AE,AB=AD$ and $\angle BAD=\angle EAC$. Then show that $BC=DE$.