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. For solve and practice worksheet and CBSE Sample paper click on : Download File 10th maths Ch Similar Triangle Guess Paper SA-1 Download File
9 Comments
mahi
27/8/2013 02:41:33 am
excellent idea
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Debabrata
27/8/2013 02:43:31 am
I hate triangles
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mahi
30/6/2015 02:00:27 am
So no need to give comment about this its ur feeling
Toshal
21/7/2014 06:55:10 am
Oh I want some questions on bpt and now I am able to crush all my tution mates planning
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Harini.M
26/7/2014 05:04:47 am
it's awesome
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Akshat
22/6/2015 03:38:32 am
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Mm
27/10/2016 06:11:58 pm
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vijeeth
31/1/2016 04:17:53 pm
increase the dificulty
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sneha
13/9/2016 09:48:24 pm
I've already learnt this problems.I want nww problems.
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