Chapter 9: Geometric Twins
When are two shapes exact copies of each other? In this chapter we learn what congruent figures are, which few measurements are enough to be sure two triangles are congruent (SSS, SAS, ASA, AAS, RHS), how to write congruence correctly, and how congruence proves that the base angles of an isosceles triangle are equal.
In this chapter you will
- recognise congruent figures
- use SSS, SAS, ASA, AAS and RHS
- write congruence with matching vertices
- find angles in isosceles and equilateral triangles
Topics
- Geometric Twins NCERT P2 1.1
Congruent figures have the same shape and size; one fits exactly over the other.
- Congruence of Triangles NCERT P2 1.2
SSS, SAS, ASA, AAS and RHS guarantee congruence; AAA and SSA do not.
- Angles of Isosceles and Equilateral Triangles NCERT P2 1.3
Angles opposite equal sides are equal.
Key words
- Congruent
- same shape and size
- Corresponding parts
- vertices, sides and angles that match when one figure is placed on the other
- SSS / SAS / ASA
- three sides; two sides and the angle between; two angles and the side between
- AAS
- two angles and a side not between them
- Hypotenuse
- the side opposite the right angle
- RHS
- right angle, hypotenuse and one side
Summary
- Congruent figures have the same shape and size; turning and flipping are allowed.
- SSS, SAS, ASA, AAS and RHS guarantee congruence of triangles; AAA and SSA do not.
- In △ABC ≅ △XYZ the order of letters shows which parts match.
- Angles opposite equal sides are equal; equilateral triangles have three 60° angles.