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Areas of Two Similar TrianglesCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! Areas of Two similar Triangles : The ratio of the areas of twoSimilar Triangles are equal to the ratio of the squares of any two corresponding sides.
Some important theorems :
Some solved examples 1) If ΔABC ~ ΔDEF such that BC = 3 cm and EF = 4 cm and the area of ΔABC = 54 cm ^{2} . Find the area of ΔDEF. Solution : Since the ratio of the areas of two similar triangles are equal to the ratio of the squares of any two corresponding sides.
⇒ Area (Δ DEF ) = ( 54 x 16 ) / 9 ⇒ Area ( Δ DEF) = 96 cm ^{2} 2) Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Find the ratio of their corresponding heights. Solution : Let ΔABC and ΔDEF be the given triangles such that AB = AC and DE = DF, ∠ A = ∠ D.
Now, AB = AC , DE = DF ⇒ AB / AC = 1 and DE / DF = 1 ⇒ AB / AC = DE / DF ⇒ AB / DE = AC / DF ( By alternendo) Thus, in triangles ABC and DEF, we have, AB / DE = AC / DF and ∠A = ∠ D ΔABC ~ ΔDEF ( By SAS ) ⇒ Area ( Δ ABC ) / Area ( ΔDEF ) = AL ^{2} / DM ^{2} ⇒ 16 / 25 = AL ^{2} / DM ^{2} ⇒ AL / DM = 4 /5 Hence, AL : DM = 4 : 5 Similarity in Triangles • Similarity in Geometry • Properties of similar triangles • Basic Proportionality Theorem(Thales theorem) • Converse of Basic Proportionality Theorem • Interior Angle Bisector Theorem • Exterior Angle Bisector Theorem • Proofs on Basic Proportionality • Criteria of Similarity of Triangles • Geometric Mean of Similar Triangles • Areas of Two Similar Triangles Covid19 has affected physical interactions between people. Don't let it affect your learning.
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