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# 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

**☛ Related Questions:**

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