NCERT Class 7 Maths Chapter 9
Geometric Twins
This chapter from Ganita Prakash Part 2 explores the concepts of congruence and similarity in geometric figures for CBSE Class 7 students. Students learn when two shapes are congruent (identical in shape and size) or similar (same shape but different sizes), and explore the criteria for congruence of triangles (SSS, SAS, ASA, RHS). The chapter connects geometry to real-life applications such as tiling and design.
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Key Terms
- Congruence
- Two geometric figures are congruent if they have the same shape and the same size. One can be placed exactly over the other to match perfectly.
- Similarity
- Two geometric figures are similar if they have the same shape but may differ in size. Corresponding angles are equal and corresponding sides are proportional.
- SSS Congruence
- Side-Side-Side congruence criterion: two triangles are congruent if all three corresponding sides are equal.
- SAS Congruence
- Side-Angle-Side congruence criterion: two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of the other.
- ASA Congruence
- Angle-Side-Angle congruence criterion: two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and included side of the other.
- Corresponding Parts
- In congruent or similar figures, the parts (sides and angles) that match up with each other when the figures are placed in the same orientation.
Frequently Asked Questions
What is the difference between congruent and similar figures?▾
Congruent figures are exactly the same in shape and size — one fits perfectly over the other. Similar figures have the same shape but not necessarily the same size — their corresponding angles are equal and corresponding sides are in the same ratio.
What are the criteria for congruence of triangles in Class 7?▾
The four criteria for triangle congruence are: SSS (all three sides equal), SAS (two sides and the included angle equal), ASA (two angles and the included side equal), and RHS (right angle, hypotenuse, and one other side equal in right-angled triangles).
If two triangles are congruent, what can we say about their sides and angles?▾
If two triangles are congruent, all their corresponding sides are equal and all their corresponding angles are equal. This is stated as CPCT — Corresponding Parts of Congruent Triangles.
What does CPCT mean in geometry?▾
CPCT stands for Corresponding Parts of Congruent Triangles. It is a theorem stating that once two triangles are proven congruent using any criterion (SSS, SAS, ASA, RHS), all their remaining corresponding sides and angles must also be equal.
Give a real-life example of congruent figures.▾
Congruent figures appear in mass-produced items such as biscuits of the same shape, tiles on a floor, stamps on a sheet, or the identical wings of a butterfly. Any two objects that are identical copies of each other in shape and size are congruent.
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