Ex 6.3, 1

Transcript

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 ∆ 𝐴𝐵𝐶 and ∆ 𝑃𝑄𝑅 ∠𝐴= ∠P ∠𝐵= ∠Q ∠𝐶= ∠R ∆ 𝐴𝐵𝐶 ∼ ∆ 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 𝐴𝐵/𝑄𝑅=2/4 = 1/2 𝐴𝐶/𝑄𝑃=3/6 = 1/2 𝐵𝐶/𝑅𝑃=2.5/5 = 1/2 Hence, 𝐴𝐵/𝑄𝑅=𝐴𝐶/𝑄𝑃=𝐵𝐶/𝑅𝑃=1/2 Therefore , using SSS similarly criterion So, ∆ 𝐴𝐵𝐶 ∼ ∆ 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 ∴ , Δ LMP and ∆𝐹𝐸𝐷are 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 ∆ 𝑀𝑁𝐿 and ∆𝑄𝑃𝑅 ∠𝑀 = ∠𝑄 =70° Also, 𝑀𝑁/𝑄𝑃=2.5/5 = 25/(5 ×10)=1/2 𝑀𝐿/𝑄𝑅=5/10=1/2 So, 𝑀𝑁/𝑃𝑄=𝑀𝐿/𝑄𝑅=1/2 Hence, by SAS similarity criterion for two triangles ∆ 𝑀𝑁𝐿∼∆𝑄𝑃𝑅 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 ∆ 𝐴𝐶𝐵 and ∆ 𝐹𝐷𝐸 ∠ A = ∠ F = 80° 𝐴𝐵/𝐹𝐷=2.5/5 = 25/(5 ×10) =1/2 𝐴𝐶/𝐹𝐸=𝐴𝐶/6 AC is not given So, 𝐴𝐵/𝐷𝐹 ≠ 𝐴𝐶/𝐸𝐹 So , ∆ 𝐴𝐶𝐵 and ∆ 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 ∆ 𝐷𝐸𝐹 ∠𝐷+∠𝐸+∠𝐹 = 180° 70°" "+80°" "+∠𝐹" = " 180° 150° +∠𝐹 = 180° ∠𝐹= 180° - 150° ∠𝐹= 30° In ∆ 𝐷𝐸𝐹 and ∆ 𝑃𝑄𝑅 ∠𝐸=∠𝑄 ∠𝐹=∠𝑅 Therefore by AA similarity criterion for two triangles ∆ 𝐷𝐸𝐹∼" " ∆ 𝑃𝑄𝑅