Last updated at March 2, 2017 by Teachoo

Transcript

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

Class 9

Important Questions for Exam - Class 9

- Chapter 1 Class 9 Number Systems
- Chapter 2 Class 9 Polynomials
- Chapter 3 Class 9 Coordinate Geometry
- Chapter 4 Class 9 Linear Equations in Two Variables
- Chapter 5 Class 9 Introduction to Euclid's Geometry
- Chapter 6 Class 9 Lines and Angles
- Chapter 7 Class 9 Triangles
- Chapter 8 Class 9 Quadrilaterals
- Chapter 9 Class 9 Areas of parallelograms and Triangles
- Chapter 10 Class 9 Circles
- Chapter 11 Class 9 Constructions
- Chapter 12 Class 9 Herons Formula
- Chapter 13 Class 9 Surface Areas and Volumes
- Chapter 14 Class 9 Statistics
- Chapter 15 Class 9 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.