If for ∆ABC and ∆DEF, the correspondence CAB ↔ EDF gives a congruence, then which of the following is not true?
(a) AC = DE
(b) AB = EF
(c) ∠A = ∠D
(d) ∠C = ∠E

Solution:

Given, the triangles ABC and DEF are congruent.

The correspondence CAB ↔ EDF gives a congruence.

We have to find the correct option.

If ∆ABC and ∆DEF are congruent, then

The sides are congruent.

AB = DF

BC = EF

AC = DE

The angles are also congruent.

∠A = ∠D

∠B = ∠F

∠C = ∠E

From the given options,

AB ≠ EF

Therefore, AB = EF is not true.

✦ Try This: ∠A + ∠B = 65° and ∠A + ∠C = 145°. Calculate each angle of the triangle

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 42

If for ∆ABC and ∆DEF, the correspondence CAB ↔ EDF gives a congruence, then which of the following is not true? (a) AC = DE, (b) AB = EF, (c) ∠A = ∠D, (d) ∠C = ∠E

Summary:

If for ∆ABC and ∆DEF, the correspondence CAB ↔ EDF gives a congruence, then AB = EF is not true.

☛ Related Questions:

• In Fig. 6.18, M is the mid-point of both AC and BD. Then: (a) ∠1 = ∠2, (b) ∠1 = ∠4, (c) ∠2 = ∠4, (d) . . . .
• If D is the midpoint of the side BC in ∆ABC where AB = AC, then ∠ADC is: (a) 60°, (b) 45°, (c) 120°, . . . .
• Two triangles are congruent, if two angles and the side included between them in one of the triangle . . . .