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Similarity Conditions Of Triangles

Published in: Mathematics
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  • Abhishek K

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This ppt is about similarity conditions of triangles which are:- 1. SAS similarity 2. SSS similarity 3. AAA/AA similarity

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    geometrical figures are said to be Similar if they have same shape but may or may not have same size, geometrical figures are said to be Congruent they have same shape and same size, >AII Congruent figures are Similar but all Similar figure may or may not be Congruen
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    SINLAR peLYGON > Two polygons are said to be similar if :- They have same number of sides. • Their corresponding angles are equal. • All corresponding sides are in proportional i.e. they are in the same ratio.
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    4.8 cm 2.4 cm C s 850 4.2 cm 700 5.0 cm D 850 2.1 cm 700 2.5 cm 1050 100 1.5 cm we have : 1050 1000 3.0 cm In quad. ABCD and quad. PQRS , ZA=ZP ZB=ZQ ZC=ZR Therefore, quad. ABCD quad. PQRS Hence, AB BC CD AD RS PS
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    OF Two triangles are similar, if: Their corresponding angles are equal and V Their corresponding sides are in the same ratio (or proportion). 'The OF sides in two equiangular triangles is always the same,
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    THALESTHKOREH line is parallel ge er2e side ef gridM51e ge ingepsecg ghe —gher sides i'? ghe sides ape divided ghe This theorem is also known as " BASIC PROPORTIONALITY THEOREM.
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    C0NDIT10Ns FOR slMILARrrY OF TRIANGLE There are three conditions for similarity of triangle : i. ii. iii. A-A-A similarity condition(angle-angle-angle) or A-A similarity condition(angle-angle) S-S-S similarity condition(side-side-side) S-A-S similarity condition (side-angle-side)
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    If one angle of a triangle is equal to one angle" the other triangle and the sides including these angles are proportional, then the two triangles are similar,
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    Given , In AGHI and ALKJ , ZH : LK 500 5 5cm ; Hl=7cm ; LK=10cm ; KJ=14cm 500 GH 5 LK 10 (by Thales theorem) 1 2 In AGHI and ALKJ 1 O Therefore, 1 2 500 (given) ACHI ALKJ 500 14 (s-a-s) Proved.

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