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Grade -10 (SEE) Math Geometry, Triangle and Quadrilateral

In the given figure prove that triangle EFJ is congruent to triangle HGI

In the given figure, EF//GH, EI//FG and FJ//GI, then prove that:

  1. ΔEFJ ≅ ΔHGI
  2. Area of parallelogram EFGH = Area of parallelogram FGIJ
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1 Answer

Tribhuvan University > Institute of Science and Technology > B.Sc. (CSIT)

Solution:

Given: EF//GH, EI//FG and FJ//GI

To prove:

  1. ΔEFJ ≅ ΔHGI
  2. Area of parallelogram EFGH = Area of parallelogram FGIJ

Proof:

SN Statements Reasons
1.

In ΔEFJ and ΔHGI

  1. ∠FEJ = ∠GHI
  2. ∠EJF = ∠HIG
  3. JF = IG

 

  1. Corresponding angles, being EF//GH
  2. corresponding angles, being FJ//GI
  3. being opposite sides of parallelogram FGIJ
2. ∴ ΔEFJ ≅ ΔHGI  By A.A.S statement.
3.  Area of ΔEFJ = area of  ΔHGI  Areas of congruent triangles, from statement 2
4. Area of Trapezium EFGI - ΔHGI = Area of Trapezium EFGI - area of ΔEFJ Subtracting equal triangles from Trapezium EFGI.
5. ∴ Area of parallelogram EFGH = Area of parallelogram FGIJ From statement (4), by whole part axiom.

Hence proved.

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