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# In Fig. 6.52, DE = IH, EG = FI and ∠ E = ∠ I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?

**Solution:**

Given, the figure represents two __triangles__ DEF and GHI.

Also, DE = IH, EG = FI

∠E = ∠I

We have to determine if the triangles DEF and HIG are __congruent__ or not.

Given, EG = FI

Adding GF on both sides,

EG + GF = FI + GF

From the figure,

EG + GF = EF

FI + GF = IG

So, EF = IG

Considering triangles DEF and HIG,

Given, DE = IH

Also, EF = IG

∠E = ∠I

The __SAS criterion__ states that If two sides of one triangle are respectively proportional to two __corresponding sides__ of another, and if the included angles are equal, then the two triangles are congruent.

By SAS rule, ∆DEF ≅ ∆HIG

**✦ Try This: **In Fig, is the pair of triangles are congruent?

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 6

**NCERT Exemplar Class 7 Maths Chapter 6 Problem 151**

## In Fig. 6.52, DE = IH, EG = FI and ∠ E = ∠ I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?

**Summary:**

In Fig. 6.52, DE = IH, EG = FI and ∠ E = ∠ I. ∆DEF ≅ ∆HIG by SAS congruence criterion.

**☛ Related Questions:**

- In Fig. 6.53, ∠1 = ∠ 2 and ∠ 3 = ∠ 4. (i) Is ∆ADC ≅ ∆ ABC? Why ? (ii) Show that AD = AB and CD = CB
- Observe Fig. 6.54 and state the three pairs of equal parts in triangles ABC and DBC. (i) Is ∆ABC ≅ ∆ . . . .
- In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT. (i) Is ∆QSR ≅ ∆RTQ? Give reasons. (ii) Is ∠PQR = ∠PRQ? G . . . .

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