Geometric Twins Class 7 Notes Maths Part 2 Chapter 1

Well-organized RBSE Class 7 Maths Notes and Part 2 Chapter 1 Geometric Twins Notes Class 7 make learning formulas much easier.

Class 7 Maths Geometric Twins Notes

Class 7 Geometric Twins Notes

→ Congruent Figures—Figures that have the same shape and size are said to be congruent. These figures can be superimposed so that one fits exactly over the other.

→ Congruence of Triangles—When two triangles have the same shape and size, we say that these are congruent.

→ The two triangles are congruent if they satisfy any one of the following conditions:
(a) SSS, (b) SAS, (c) ASA, (d) AAS, (e) RHS.

• If two triangles have the same side lengths, then they are congruent. We call this the SSS (Side-Side-Side) condition for congruence.
• When two sides and the angle between them are the same in both triangles, the triangles are congruent. This is known as the SAS (Side-Angle-Side) condition for congruence.
• Two triangles are said to be congruent if their two corresponding angles and a side are equal. This condition is referred to as the ASA (Angle-Side-Angle) condition for congruence.
• The two triangles have two equal angles and a corresponding side that is not between those angles, is known as the AAS (Angle-Angle-Side) condition. The AAS condition always ensures congruence.
• When a side and a hypotenuse of a right-angled triangle are equal to a side and the hypotenuse of another right-angled triangle, we say that the RHS (Right Hypotenuse Side) condition is satisfied. The RHS condition also guarantees congruence.

→ The congruence of two triangles ∆ ABC and ∆ XYZ is written as follows :
∆ ABC = ∆ XYZ. By writing this we mean that:

• the first vertex of ∆ ABC matches the first vertex of ∆ XYZ,
• the second vertex of ∆ ABC matches the second vertex of ∆ XYZ, and
• the third vertex of ∆ ABC matches the third vertex of ∆ XYZ.

→ When two triangles are congruent, then their corresponding parts (sides and angles) are equal. This is called C.P.C.T.

→ In an isosceles triangle, angles opposite to equal sides are equal.

→ In an equilateral triangle all the sides are equal and all the three angles are equal, so each angle is 60°.

→ Congruent triangles can be seen in various constructions and designs from ancient to modem times.