1Fill in the blank: in an equilateral triangle all the angles are ................ .
2Fill in the blank: a triangle whose sides are all of different lengths is called a ................ triangle.
3Fill in the blank: on the basis of their sides, triangles are of ................ kinds.
4Fill in the blank: if one angle of a triangle measures more than \( 90^\circ \), the triangle is called an ................ triangle.
5Fill in the blank: a triangle that is equilateral by its sides is always a ................ triangle by its angles.
6Classify these triangles by the lengths of their sides. The first has sides of 6 cm, 6 cm and 6 cm. The second has sides of 7 cm, 7 cm and 4 cm. The third has sides of 5 cm, 6 cm and 8 cm.
7Classify these triangles by the sizes of their angles. The first has angles of \( 40^\circ, 60^\circ \) and \( 80^\circ \). The second has angles of \( 90^\circ, 55^\circ \) and \( 35^\circ \). The third has angles of \( 110^\circ, 40^\circ \) and \( 30^\circ \).
8Draw a rectangle ABCD and both of its diagonals AC and BD, which cross at O. From the triangles that appear, name two acute angled, two right angled and two obtuse angled triangles.
9Draw a triangle POQ in which \( \angle POQ = 120^\circ \), then measure the other two angles with a protractor. What kind of triangle is it?
10Draw a triangle LMN in which \( \angle LNM = 90^\circ \). What kind of triangle is it, and what are the other two angles like?
11State whether each of these is true or false. (a) All the sides of a square are equal. (b) A square and a rhombus are the same thing.
12Classify these quadrilaterals from their measurements. (a) Quadrilateral ABCD has four sides of 3 cm and angles of \( 60^\circ \) and \( 120^\circ \). (b) Quadrilateral HFEG has opposite sides of 4 cm and 2 cm and four angles of \( 90^\circ \). (c) Quadrilateral KNML has opposite sides that are equal and parallel, but its angles are not \( 90^\circ \).
13Anjali said, "A quadrilateral with four equal sides is a rectangle." Anjal said, "A quadrilateral whose opposite sides are equal and whose four angles are \( 90^\circ \) is a rectangle." Whose statement is correct, and why?
14Two pairs of parallel lines cross to form the quadrilateral IJKL. (a) What kind of quadrilateral is it? (b) If \( \angle ILK \) and \( \angle LKJ \) are both \( 90^\circ \), what does it become? (c) When does it become a square?
15Why can a triangle never have two right angles?
16Can we say that every rectangle is a parallelogram? Give a reason.
17Write down the difference between a rhombus and a trapezium.
18A triangle has sides of 5 cm, 5 cm and 8 cm, and its largest angle measures \( 106^\circ \). Classify it in both ways.
19In a quadrilateral ABCD, the perpendiculars AX and BY drawn from A and B to the side DC are equal in length. What does this tell us?