Ex 6.3, 1 - State which pairs of triangles are similar. - Ex 6.3

  1. Chapter 6 Class 10 Triangles
  2. Serial order wise
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Ex 6.3,1 (i) State which pairs of triangles in figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form In βˆ† 𝐴𝐡𝐢 and βˆ† 𝑃𝑄𝑅 ∠𝐴= ∠P ∠𝐡= ∠Q ∠𝐢= ∠R βˆ† 𝐴𝐡𝐢 ∼ βˆ† 𝑃𝑄𝑅 Ex 6.3, 1 (ii) State which pairs of triangles in figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form Finding ratio of sides 𝐴𝐡/𝑄𝑅=2/4 = 1/2 𝐴𝐢/𝑄𝑃=3/6 = 1/2 𝐡𝐢/𝑅𝑃=2.5/5 = 1/2 Hence, 𝐴𝐡/𝑄𝑅=𝐴𝐢/𝑄𝑃=𝐡𝐢/𝑅𝑃=1/2 Therefore , using SSS similarly criterion So, βˆ† 𝐴𝐡𝐢 ∼ βˆ† 𝑄𝑅𝑃 Ex 6.3, 1(iii) State which pairs of triangles in figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form Finding ratio of sides 𝑀𝑃/𝐸𝐷=2/4 = 1/2 𝑃𝐿/𝐷𝐹=3/6 = 1/2 𝐿𝑀/𝐹𝐸=2.7/5 Here, the ratio of corresponding sides of both the triangles is not same ∴ , Ξ” LMP and βˆ†πΉπΈπ·are not similar . Ex 6.3, 1 (iv) State which pairs of triangles in figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form In βˆ† 𝑀𝑁𝐿 and βˆ†π‘„π‘ƒπ‘… βˆ π‘€ = βˆ π‘„ =70Β° Also, 𝑀𝑁/𝑄𝑃=2.5/5 = 25/(5 Γ—10)=1/2 𝑀𝐿/𝑄𝑅=5/10=1/2 So, 𝑀𝑁/𝑃𝑄=𝑀𝐿/𝑄𝑅=1/2 Hence, by SAS similarity criterion for two triangles βˆ† π‘€π‘πΏβˆΌβˆ†π‘„π‘ƒπ‘… Ex 6.3, 1(v) State which pairs of triangles in figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form In βˆ† 𝐴𝐢𝐡 and βˆ† 𝐹𝐷𝐸 ∠ A = ∠ F = 80Β° 𝐴𝐡/𝐹𝐷=2.5/5 = 25/(5 Γ—10) =1/2 𝐴𝐢/𝐹𝐸=𝐴𝐢/6 AC is not given So, 𝐴𝐡/𝐷𝐹 β‰  𝐴𝐢/𝐸𝐹 So , βˆ† 𝐴𝐢𝐡 and βˆ† 𝐹𝐷𝐸 are not similar . Ex 6.3, 1 (vi) State which pairs of triangles in figure are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form In βˆ† 𝐷𝐸𝐹 ∠𝐷+∠𝐸+∠𝐹 = 180Β° 70Β°" "+80Β°" "+∠𝐹" = " 180Β° 150Β° +∠𝐹 = 180Β° ∠𝐹= 180Β° - 150Β° ∠𝐹= 30Β° In βˆ† 𝐷𝐸𝐹 and βˆ† 𝑃𝑄𝑅 ∠𝐸=βˆ π‘„ ∠𝐹=βˆ π‘… Therefore by AA similarity criterion for two triangles βˆ† 𝐷𝐸𝐹∼" " βˆ† 𝑃𝑄𝑅

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