Tag: congruence
Questions Related to congruence
ABCD is a tetrahedron and O is any point. If the lines joining O to the vertices meet the opposite at P, Q, R and S, then $\frac{OP}{AP}+\frac{OQ}{BQ}+\frac{OR}{CR}+\frac{OS}{DS}=2$.
It is given that $\Delta ABC \sim \Delta PQR$ with $\dfrac{BC}{QR} = \dfrac{1}{3}$. Then $\dfrac{ar (\Delta PQR)}{ar (\Delta ABC)}$ is equal to
$CM$ and $RN$ are respectively the medians of $\triangle {ABC}$ and $\triangle{PQR}$. If $\triangle {ABC}\sim \triangle{PQR}$, then
$\cfrac{CM}{RN}=\cfrac{AB}{PQ}$
In a square $ABCD$, the bisector of the angle $BAC$ cut $BD$ at $X$ and $BC$ at $Y$ then triangles $ACY, ABX$ are similar.
Assume that, $\Delta RST \sim \Delta XYZ$. Complete the following statement.
Consider the following statements:
(1) If three sides of triangle are equal to three sides of another triangle, then the triangles are congruent.
(2) If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.
If in trianges $ABC$ and $DEF$, $\cfrac{AB}{DE}=\cfrac{BC}{FD}$, then they will be similar, when:
In $\triangle PQR,$ $PQ=4$ cm, $QR=3$ cm, and $RP=3.5$ cm. $\triangle DEF$ is similar to $\triangle PQR.$ If $EF=9$ cm, then what is the perimeter of $\triangle DEF: ?$
The perimeter of two similar triangles are $24$ cm and $16$ cm, respectively. If one side of the first triangle is $10$ cm, then the corresponding side of the second triangle is