Class 7 Maths - HARYANA
Geometric Twins
The chapter 'Geometric Twins' in Class 7 Mathematics, prescribed by the Board of School Education Haryana (BSEH), explores the fascinating world of congruence in shapes. Students learn when two geometric figures, particularly line segments, angles, and triangles, are exact twins in terms of shape and size. The chapter introduces fundamental criteria for triangle congruence such as SSS, SAS, ASA, and RHS. Understanding these concepts is crucial for building a strong foundation in geometry, enabling students to solve complex geometric proofs and rider problems in board examinations.
Start Learning FreeKey Concepts
Congruent Figures
Two geometric figures are congruent if they have the exact same shape and size, meaning one can superimpose completely over the other.
Congruence of Line Segments
Two line segments are congruent if and only if they are of equal length.
Congruence of Angles
Two angles are congruent if and only if they have the same measure in degrees.
SSS (Side-Side-Side) Criterion
If three sides of one triangle are equal to the corresponding three sides of another triangle, then 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, 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 the Haryana (BSEH) Class 7 Mathematics examinations, this chapter typically carries around 6 to 8 marks. Common question types include identifying congruent shapes, applying triangle congruence criteria (SSS, SAS, ASA, RHS) to prove two triangles are congruent, and finding unknown angles or sides using the properties of congruent figures.
Frequently Asked Questions
What is the difference between similarity and congruence?
Similar figures have the same shape but can be of different sizes (like a small photo and its enlarged copy), whereas congruent figures ('geometric twins') have both the exact same shape and the exact same size.
Is 'AAA' a valid criterion for the congruence of triangles?
No, AAA (Angle-Angle-Angle) is not a valid criterion for congruence because two triangles can have the exact same angles while being of completely 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. If the angle is not between the given sides, the triangles might not be congruent even if the two sides and an angle are equal.
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