In a parallelogram ABCD, P and Q are the points on line DB such that PD = BQ show that APCQ is a parallelogram.

Your friend draws a figure such as this on a piece of paper.
You don't know what it is, and stand at the board. She has to describe the figure to you so that you draw exactly the same figure on the board.
You both know rectangles, so it is easy to describe and draw a rectangle. The rest are not easy.
Can we describe any such shape we can ever think of, in a way that another person
hearing it can reproduce it exactly?
Yes, yes, yes! Now, isn't that exciting? The answer is so simple that it is breathtaking.
We describe different shapes by their properties.

Take three different colour sheets; place on over the other and draw a triangle on the top sheet. Cut the sheets to get triangles of different colour which are identical. Mark the vertices and the angles as shown. Place the interior angles ㄥ1, ㄥ2 and ㄥ3 on a straight line, adjacent to each other, without leaving any gap. What can you say about the total measure of the three angles ㄥ1, ㄥ2 and ㄥ3?


Can you use the same figure to explain the "Exterior angle property" of a triangle?
If a side of a triangle is stretched, the exterior angle so formed is equal to the sum of the two remote interior angles.

If O is the centre of the circle and ㄥABC = 30° then find ㄥAOC.

In the given figure, ㄥCAB = 25°, find ㄥBDC, ㄥDBA and ㄥCOB

Construct the ΔLMN such that LM = 7.5cm, MN = 5cm and LN = 8cm. Locate its centroid.

Draw and locate the centroid of the triangle ABC where right angle at A, AB = 4cm and AC = 3cm

Draw the \(\triangle \)ABC , where AB = 6 cm, B = 110° and AC = 9 cm and construct the centroid.

Construct the ΔPQR such that PQ = 5cm, PR= 6cm and ㄥQPP = 60° and locate its centroid.

Construct an equilateral triangle of side 6cm and locate its centroid and also its incentre. What do you observe from this?