Uttar Pradesh Board Solutions for Chapter: Triangle, Exercise 25: Ability Exercise 5

$AD, BE$ and $CF$ are the medians of any $∆ABC$ and $G$ its centroid. What is the type of $∆GBC$? Investigate through drawing an isosceles triangle.

$AD, BE$ and $CF$ are the medians of any $∆ABC$ and $G$ its centroid. What is the type of $∆GBC$? Investigate through drawing an equilateral triangle.

Draw a perpendicular bisector $l$ of the line-segment $AB$. Take any point $P$ on $l$ and measure $PA$ and $PB$.

Construct a triangle $ABC$, whose base is $7 \mathrm{cm}, \angle B=60°$ and the sum of two sides is $9 \mathrm{cm}$.

Construct a triangle $ABC$, whose one angle is $120°$ and the two sides are $5 \mathrm{cm}$ and $6 \mathrm{cm}$, respectively, then find its circumcentre of the triangle.

Construct an equilateral triangle, whose side is $6 \mathrm{cm}$, then find the centroid of the triangle and find the distance between the vertex and centroid.

The ratio of the sides of a triangle $PQR$ is $4:5:6$ construct a triangle $ABC$ similar to $PQR$. Whose base is $8 \mathrm{cm}$.

In the enclosed figure the area of $DEF$ will be:

$D, E, F$ are the mid-point of the sides.