Mathematics
In a triangle PQR, L and M are two points on the base QR, such that ∠LPQ = ∠QRP and ∠RPM = ∠RQP. Prove that :
(i) △PQL ~ △RPM
(ii) QL × RM = PL × PM
(iii) PQ2 = QR × QL
Related Questions
The dimensions of the model of a multistoreyed building are 1 m by 60 cm by 1.20 m. If the scale factor is 1 : 50, find the actual dimensions of the building.
Also, find :
(i) the floor area of a room of the building, if the floor area of the corresponding room in the model is 50 sq. cm.
(ii) the space (volume) inside a room of the model, if the space inside the corresponding room of the building is 90 m3.
On a map, drawn to a scale of 1 : 20000, a rectangular plot of land ABCD has AB = 24 cm and BC = 32 cm. Calculate :
(i) the diagonal distance of the plot in kilometre.
(ii) the area of the plot in sq. km.
A triangle ABC with AB = 3 cm, BC = 6 cm and AC = 4 cm is enlarged to △DEF such that the longest side of △DEF = 9 cm. Find the scale factor and hence, the lengths of the other sides of △DEF.
Two isosceles triangles have equal vertical angles. Show that the triangles are similar.
If the ratio between the areas of these two triangles is 16 : 25, find the ratio between their corresponding altitudes.