NCERT Solutions Class 7 Maths Chapter 9 — Congruence & Symmetry

Solution:

Step 1: The definition of congruence in geometry means that two figures are exactly alike.

Step 2: This implies they must have both the same shape and the same size.

Step 3: If one figure can be moved (translated, rotated, reflected) and perfectly overlap the other, they are congruent. Option A provides the most complete and accurate definition.

Solution:

Step 1: Congruence refers to figures having the same shape and size.

Step 2: For line segments, their 'shape' is always a straight line, so the crucial factor for congruence is their 'size'.

Step 3: The 'size' of a line segment is its length. Therefore, two line segments are congruent if they have the same length.

Solution:

Step 1: Angles are defined by the amount of rotation between two rays meeting at a common vertex.

Step 2: The 'size' or 'opening' of an angle is determined by its measure, typically in degrees.

Step 3: For two angles to be congruent, their measures must be exactly the same. The lengths of the arms do not affect the angle's measure.

Solution:

Step 1: The problem states that all three corresponding sides of ΔABC and ΔXYZ are equal: AB = XY, BC = YZ, and CA = ZX.

Step 2: When three sides of one triangle are equal to the three corresponding sides of another triangle, the triangles are congruent by the SSS (Side-Side-Side) criterion.

Step 3: Therefore, the SSS congruence criterion applies.

Solution:

Step 1: We are given two sides (PQ and QR) and the included angle (∠PQR) of ΔPQR.

Step 2: Similarly, we are given two sides (DE and EF) and the included angle (∠DEF) of ΔDEF.

Step 3: Since PQ = DE, ∠PQR = ∠DEF, and QR = EF, the two triangles are congruent by the SAS (Side-Angle-Side) criterion, as the angle is included between the two sides.