**10th Triangle (Similarity) : Problems and solution to excel in exam**

Similar figures: “Two similar figures have the same shape but not necessarily the same sizes are called similar figures. “ This verifies that congruent figures are similar but the similar figures need not be congruent.

Conditions for similarity of polygon: 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 (or proportion).

Note: The same ratio of the corresponding sides is referred to as the scale factor (or the Representative Fraction) for the polygons.

Equiangular triangles: If corresponding angles of two triangles are equal, then they are known as equiangular triangles.

A famous Greek mathematician Thales gave an important truth relating to two equiangular triangles which is as follows: “The ratio of any two corresponding sides in two equiangular triangles is always the same.”

Q. The Basic Proportionality Theorem (now known as the Thales Theorem) : “If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. “ [Prove it.]

Q. The converse of The Basic Proportionality Theorem: If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side. [Prove it by contradiction methods]

Q. In a triangle ABC, E and F are point on AB and AC and EF || BC. Prove that AB/AE = AC/AF

Q. Prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

Q. Prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Q. In a triangle ABC, E and F are point on AB and AC Such that AE/EB = AF/FC and <AEF =<ACB. Prove that ABC is an isosceles Triangle.

Q. In a trapezium ABCD , AB || DC and E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB .Show that AE/ ED = BF /FC [join AC to intersect EF at G]

Q. In a trapezium ABCD , AB || DC and its diagonals intersect each other at the point O. Show that AO/ BO = CO/DO

Q. The diagonals of a quadrilateral ABCD intersect each other at the point O such that AO/ BO = CO/DO . Show that ABCD is a trapezium.

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10th maths Ch Similar Triangle Guess Paper SA-1

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