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SUMMARY SIMILAR TRIANGLE Two triangle ABC and DEF are said to be similar if their i) Corresponding Angles are equal. I.e. β A=β π·, β π΅ = β πΈ, β πΆ = β F And, ii) Corresponding Sides are proportional. i) (AAA Similarity)If two triangles are equiangular, then they are similar. ii) (SSS Similarity)If the corresponding sides of two triangles are proportional, then they are similar. iii) (SAS Similarity)If in two triangles ,one pair of corresponding sides are proportional and the included angles are equal then the two triangle are similar THALES THEOREM (BASIC PROPORTIONALITY THEOREM) Statement: 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. AREA OF SIMILAR TRIANGE Two triangles ABD and PQR such that ΞABC~ΞPQR ππ(π΄π΅πΆ) π΄π΅ 2 π΅πΆ 2 πΆπ΄ 2 =( ) =( ) =( ) ππ(πππ ) ππ ππ π π
OBJECTIVE 1)
In the following figure AE is perpendicular to BC,D is the midpoint of BC then x is equal to: 1
a) π (π 2 β π2 β b) c) d)
2)
β+π
π2 4
)
3 π+πββ 2 π2 +π 2 +π2 βπ 2 2
ππ
Two triangles ABC and PQR are similar, If BC:CA:AB=1:2:3 then ππ is: 2
a)3
1
π) 2
π)
1
β2
2
π) 3
3)
In a triangle ABC if an angle B=90o and D is the point in BC such that BD=2DC then a) AC2=AD2+3CD2 b) AC2=AD2+5CD2 2 2 2 c)AC =AD +7CD d) AC2=AB2+5BD2
4)
P and Q are the mid points of the sides AB and BC respectively of the triangle ABC, the Right angle triangle at B then, HURRY!! Visit our portal and get your NCERT Solutions UPDATED 2021-22. These all very essential for your exam preparation