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Ex 8.1, 11 - In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF - Ex 8.1

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Ex 8.1, 11 - Chapter 8 Class 9 Quadrilaterals - Part 2

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Ex 8.1, 11 - Chapter 8 Class 9 Quadrilaterals - Part 3

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Ex 8.1, 11 - Chapter 8 Class 9 Quadrilaterals - Part 4

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Ex 8.1, 11 - Chapter 8 Class 9 Quadrilaterals - Part 5

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Ex 8.1, 11 - Chapter 8 Class 9 Quadrilaterals - Part 6

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Ex 8.1, 11 In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to vertices D, E and F respectively .Show that quadrilateral ABED is a parallelogram Given: Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF To prove: ABED is a parallelogram Proof: Given that AB = DE and AB ∥ DE. ⇒ One pair of opposite sides are equal and parallel to each other ∴ ABED is a parallelogram Hence proved Ex 8.1, 11 In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that (ii) quadrilateral BEFC is a parallelogram Given that BC = EF and BC ∥ EF. ⇒One pair of opposite sides are equal and parallel to each other ∴ BEFC is a parallelogram Hence proved Ex 8.1, 11 In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that (iii) AD ∥ CF and AD = CF From part(i), we proved that ABED is a parallelogram So, AD = BE and AD ∥ BE From part(ii) , we proved that BEFC is a parallelogram So, BE = CF and BE ∥ CF Hence From (1) & (2) ∴ AD = CF and AD ∥ CF Ex 8.1, 11 In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that (iv) quadrilateral ACFD is a parallelogram In part (iii) we proved that AD = CF and AD ∥ CF ⇒One pair of opposite sides are equal and parallel to each other ∴ ACFD is a parallelogram Therefore, quadrilateral ACFD is a parallelogram. Ex 8.1, 11 In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that (v) AC = DF From part(iv), ACFD is a parallelogram So, AC = DF Hence proved Ex 8.1, 11 In Δ ABC and Δ DEF, AB = DE, AB ∥ DE, BC = EF and BC ∥ EF. Vertices A, B and C are joined to vertices D, E and F respectively .Show that (vi) Δ ABC ≅ Δ DEF. In ΔABC and ΔDEF, AB = DE BC = EF AC = DF ∴ ΔABC ≅ ΔDEF

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.