For the following statments state whether true (T) or false(F):
Any two rectangles are similar.
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False.Solution:
Two rectangles are similar if their cirresponding sides are proportional.
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The corresponding sides of two similar triangles ABC and DEF are BC = 9.1cm and EF = 6.5cm. If the rerimeter of $\triangle\text{DEF}$ is 25cm, find the perimeter of $\triangle\text{ABC}.$
Two triangles DEF and GHK are such that $\angle\text{D}=48^\circ$ and $\angle\text{H}=57^\circ.$ If $\triangle\text{DEF}\sim\triangle\text{GHK}$ then find the measure of $\angle\text{F}.$
A vertical pole of lenght 7.5m casts a shadow 5m long on the ground and at the same time a tower casts a shadow 24m long. Find the height of the tower.
For the following statments state whether true (T) or false(F):
The ratio of the areas of two similar triangles is equal to the ratio of their corresponding angle-bisector segments.
In the given figure, side BC of $\triangle\text{ABC}$ is bisected at D and O is any point on AD. BO and CO produced meet AC and AB at E and F respectively, and AD is produced to X so that D is the midpoint of OX Prove that AO : AX = AF : AB and show that EF || BC.
If the lengths of the sides BC, CA and AB of a $\triangle\text{ABC}$ are a, b and c respectively and AD is the bisectore of $\angle\text{A}$ then find the lengths of BD and DC.
D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that DE || BC:
AD = (7x - 4)cm, AE = (5x - 2)cm, DB = (3x + 4)cm and EC = 3x cm.