Exercise

Name any two altitudes of the adjoining $∆DEF$.

Tom made a design (figure below) similar to one he saw on a building. In the figure, $∆AEC$, $∆AFC$ are right-angled triangles, right-angled at $E$ and $F$. $AF$ and $CE$ intersects at $B$. $BD\perp AC$.

Which of the following is/are altitude(s) of $∆ABC$?

Show the sum of exterior angles of a triangle is $360°$ . Find whether or not the same result is valid for any convex polygon.

$O$ is a point in the exterior of $△ABC$. What symbol $>, <$ or $=$ will you use to complete the statement $OA+OB$ _____ $AB$? Write two other similar statements and show that $OA+OB+OC>\frac{1}{2}\left(AB+BC+CA\right)$.

A triangle can have two obtuse angles.

A cuboid with given sides is shown below.

Which of the following can be another way of representing the cuboid?

Rajat arranged some cubes as below.

How many cubes did he use?

Mini has two identical cubes. She joins  the cubes firmly and carefully, without leaving any gap or overlap between the joint faces the edges or the vertices so that she gets a single piece of the solid.

How many faces does the resulting solid have?