Class 7 Maths - CBSE
Geometric Twins
The chapter 'Geometric Twins' in Class 7 Mathematics focuses on the fascinating world of congruence, where shapes are exact duplicates of each other in both shape and size. Students learn the fundamental criteria for triangle congruence, including SSS, SAS, ASA, and RHS postulates. Understanding these geometric twins is essential as it forms the backbone of advanced geometry, spatial reasoning, and proofs in higher classes. In CBSE board exams, this chapter carries significant weight, typically contributing 6 to 8 marks through direct application questions and proof-based problems.
Start Learning FreeKey Concepts
Congruent Figures
Two geometric figures are congruent if they have exactly the same shape and size, meaning one can superimpose over the other perfectly.
SSS (Side-Side-Side) Criterion
If three sides of one triangle are equal to the corresponding three sides of another triangle, the two triangles are congruent.
SAS (Side-Angle-Side) Criterion
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, they are congruent.
ASA (Angle-Side-Angle) Criterion
If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
RHS (Right angle-Hypotenuse-Side) Criterion
If in two right-angled triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, the triangles are congruent.
Important Formulas
Board Exam Info
In CBSE Class 7 Mathematics examinations, this chapter typically carries about 6-8 marks. Common question types include identifying congruence criteria from given figures, proving triangle congruence using SSS, SAS, ASA, or RHS, and using CPCTC to find unknown sides or angles.
Frequently Asked Questions
What is the difference between similar and congruent figures?
Congruent figures have the exact same shape and size, whereas similar figures have the same shape but can be of different sizes.
Why is the 'included angle' important in the SAS criterion?
The included angle must be the exact angle formed between the two given sides; otherwise, the triangles may not be congruent.
What does CPCTC stand for and how is it used?
CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent'. Once you prove two triangles are congruent, you can use CPCTC to state that their matching sides and angles are also equal.
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