In Fig.7.6, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that ∆ ABC ≅ ∆ DEF.
Solution:
Given, BA ⊥ AC and DE ⊥ DF
BA = DE
BF = EC
We have to show that the triangles ABC and DEF are congruent.
Considering triangles ABC and DEF,
Since BA ⊥ AC, ∠A = 90°
Since DE ⊥ DF, ∠D = 90°
Given, BF = EC
Adding CF on both sides,
BF + CF = EC + CF
From the figure,
BC = BF + CF
EF = CF + EC
So, BC = EF
Given BA = DE
By RHS criterion, ∆ ABC ≅ ∆ DEF
Therefore, the triangles ABC and DEF are congruent.
✦ Try This: In the given figure, DE∣∣BC and DE:BC = 3:5. Calculate the ratio of areas of ΔADE and the trapezium BCED.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7
NCERT Exemplar Class 9 Maths Exercise 7.3 Problem 4
In Fig.7.6, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that ∆ ABC ≅ ∆ DEF
Summary:
In Fig.7.6, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. It is shown that ∆ ABC ≅ ∆ DEF by RHS criterion
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