In the following pairs of triangles of Fig. 6.47, the lengths of the sides are indicated along the sides. By applying SSS congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.

Solution:

Given, the figures represent different forms of triangles.

We have to apply SSS congruence criterion to each triangle.

We have to write the congruent triangles in symbolic form.

Side-Side-Side congruence rule states that if three sides of one triangle are equal to three corresponding sides of another triangle, then the triangles are congruent.

All the three sides of two triangles ABC and LMN are equal.

Therefore, ∆ABC ≅ ∆NLM

All the three sides of two triangles are equal.

Therefore, ∆LMN ≅ ∆GHI

All the three sides of two triangles are equal.

Therefore, ∆LMN ≅ ∆LON

Common side = XY

All the three sides of two triangles are equal.

Therefore, ∆ZYX ≅ ∆WXY

All the three sides of two triangles are equal.

Therefore, ∆OAB ≅ ∆DOE

Common side = SU

All the three sides of two triangles are equal.

Therefore, ∆STU ≅ ∆SVU

Common side = PR

All the three sides of two triangles are equal.

Therefore, ∆PSR ≅ ∆RQP

All the three sides of two triangles are equal.

Therefore, ∆STU ≅ ∆PQR

✦ Try This: Without drawing the triangles write all six pairs of equal measures in each of the following pairs of congruent triangles. ∆SUT ≅ ∆GHI

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

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NCERT Exemplar Class 7 Maths Chapter 6 Problem 143

In the following pairs of triangles of Fig. 6.47, the lengths of the sides are indicated along the sides. By applying SSS congruence criterion, determine which triangles are congruent. If congruent, write the results in symbolic form.

Summary:

a) ∆ABC ≅ ∆NLM, b) ∆LMN ≅ ∆GHI, c) ∆LMN ≅ ∆LON, d) ∆ZYX ≅ ∆WXY, e) ∆OAB ≅ ∆DOE, f) ∆STU ≅ ∆SVU, g) ∆PSR ≅ ∆RQP, h) ∆STU ≅ ∆PQR

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☛ Related Questions:

• ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (Fig. 6.48). (a) State t . . . .
• In Fig. 6.49, it is given that LM = ON and NL = MO. (a) State the three pairs of equal parts in the . . . .
• Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = . . . .