Draw rough sketches for the following : (a) In \[\Delta ABC\], BE is a median. (b) In \[\Delta PQR,PQ\] and PR are altitudes of the triangle. (c) In \[\Delta XYZ,YL\] is an altitude in the exterior of the triangle.
Is it possible to have a triangle with the following sides? (i) \[\text{2 cm},\text{ 3 cm},\text{ 5 cm}\] (ii) \[\text{3 cm},\text{ 6 cm},\text{ 7 cm}\] (iii) \[\text{6 cm},\text{ 3 cm},\text{ 2 cm}.\]
A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
Which of the following can be the sides of a right triangle? (i) \[\text{2}.\text{5 cm}\], \[\text{6}.\text{5 cm}\], \[\text{6 cm}\]. (ii) \[\text{2 cm}\], \[\text{2 cm}\], \[\text{5 cm}\]. (iii) \[\text{1}.\text{5 cm}\], \[\text{2 cm}\], \[\text{2}.\text{5 cm}\]. In the case of right-angled triangles, identify the right angles.
A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
Angles Q and R of a \[\Delta PQR\] are \[\text{2}{{\text{5}}^{o}}\] and \[\text{6}{{\text{5}}^{o}}\]. Write which of the following is true: (i) \[P{{Q}^{2}}+Q{{R}^{2}}=R{{P}^{2}}\] (ii) \[P{{Q}^{2}}+R{{P}^{2}}=Q{{R}^{2}}\] (iii) \[R{{P}^{2}}+Q{{R}^{2}}=P{{Q}^{2}}\]