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:
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