Telangana Board Solutions for Chapter: Triangles, Exercise 5: EXERCISE

$\mathrm{AD}$ is an altitude of an isosceles triangle $\mathrm{ABC}$ in which $\mathrm{AB}=\mathrm{AC}$. Show that: $\mathrm{AD}$ bisects $\angle \mathrm{A}$.

Two sides $\mathrm{AB}, \mathrm{BC}$ and median $\mathrm{AM}$ of one triangle $\mathrm{ABC}$ are respectively equal to sides $\mathrm{PQ}$ and $\mathrm{QR}$ and median $\mathrm{PN}$ of $∆\mathrm{PQR}$ (see figure). Show that: $∆\mathrm{ABM}\cong ∆\mathrm{PQN}$.

Two sides $\mathrm{AB}, \mathrm{BC}$ and median $\mathrm{AM}$ of one triangle $\mathrm{ABC}$ are respectively equal to sides $\mathrm{PQ}$ and $\mathrm{QR}$ and median $\mathrm{PN}$ of  $∆\mathrm{PQR}$ (see figure). Show that: $∆\mathrm{AB}C\cong ∆\mathrm{PQ}R$.

$\mathrm{BE}$ and $\mathrm{CF}$ are two equal altitudes of a triangle $\mathrm{ABC}$. Using R.H.S congruence rule, prove that the triangle $\mathrm{ABC}$ is isosceles.

$∆\mathrm{ABC}$ is an isosceles triangle in which $\mathrm{AB}=\mathrm{AC}$. Show that $\angle \mathrm{B}=\angle \mathrm{C}$ (Hint: Draw $\mathrm{AP}\perp \mathrm{BC}$).

$∆\mathrm{ABC}$ is an isosceles triangle in which $\mathrm{AB}=\mathrm{AC}$. Side $\mathrm{BA}$ is produced to $D$ such that $\mathrm{AD}=\mathrm{AB}$ (see figure). Show that $\angle \mathrm{BCD}$ is a right angle.

$\mathrm{ABC}$ is a right angle triangle in which $\angle \mathrm{A}=90°$ and $\mathrm{AB}=\mathrm{AC}$. Show that $\angle \mathrm{B}=\angle \mathrm{C}$.

Show that the angles of an equilateral triangle are $60°$ each.