91Ó°ÊÓ

Fill in the blanks using the correct word given in brackets : (i) All circles are . (congruent, similar) (ii) All squares are (similar, congruent) (iii) All triangles are similar. (isosceles, equilateral) (iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are . (equal, proportional)

All the congruent figures are similar but the converse is not true.

Diagonals AC and BD of a trapezium ABCD with \(\mathrm{AB}\) II DC intersect each other at the point \(\mathrm{O}\). Using a similarity criterion for two triangles, show that \(\frac{\mathrm{OA}}{\mathrm{OC}}=\frac{\mathrm{OB}}{\mathrm{OD}}\).

Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (i.e., proportion).

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

If in two triangles, two angles of one triangle are respectively equal to the two angles of the other triangle, then the two triangles are similar (AA similarity criterion).

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in the same ratio (proportional), then the triangles are similar (SAS similarity criterion).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.