By which of the following criteria two triangles cannot be proved congruent?
(a) AAA
(b) SSS
(c) SAS
(d) ASA

Solution:

We have to find the criteria by which two triangles cannot be proved congruent.

(i) AAA - Angle-Angle-Angle congruence rule

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

(ii) SSS - Side-Side-Side Congruence rule

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.

(iii) SAS - Side-Angle-Side congruence rule

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.

(iv) ASA - Angle-Side-Angle congruence rule

ASA congruence criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be congruent".

From the above definition,

AAA criterion implies that if three angles of a two triangles are equal, does not mean that two triangles will fit exactly on each other.

Therefore, the required criteria is AAA.

✦ Try This: If the exterior angle of a triangle is 130° and its interior opposite angles are equal, then measure of each interior opposite angle is

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

NCERT Exemplar Class 7 Maths Chapter 6 Problem 47

By which of the following criteria two triangles cannot be proved congruent? (a) AAA, (b) SSS, (c) SAS

Summary:

By AAA criteria two triangles cannot be proved congruent.

☛ Related Questions:

• If ∆PQR is congruent to ∆STU (Fig. 6.20), then what is the length of TU? (a) 5 cm, (b) 6 cm, (c) 7 c . . . .
• If ∆ABC and ∆DBC are on the same base BC, AB = DC and AC = DB (Fig. 6.21), then which of the followi . . . .
• The ________ triangle always has altitude outside itself. Fill in the blanks to make the statement t . . . .