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MathematicsClass 7Geometric

Geometric | Class 7 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 5 min read

Geometric – this guide gives you a concise, exam-ready overview of Geometric from Class 7 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

1.1 Geometric Twins

This section introduces the concept of congruence through the example of recreating a symbol seen on a signboard. The problem posed is how to exactly recreate the symbol on another board. One method is tracing the outline on tracing paper, but this is impractical for large symbols. The alternative is to take measurements that allow exact reconstruction. The symbol's corner points are named (e.g., points A, B, C), and the question arises whether knowing just the arm lengths AB and BC is sufficient to recreate the figure exactly. It is observed that multiple different shapes can be formed with the same two arm lengths, so these lengths alone do not guarantee an exact replica. To fix the shape and size, the measure of the angle between the arms, ∠ABC, is also needed along with the two arm lengths. With AB = 4 cm, BC = 8 cm, and ∠ABC = 80°, the symbol can be exactly drawn. Figures that are exact copies of each other, having the same shape and size, are called congruent figures. Congruent figures can be superimposed exactly, one over the other. The section explains that while checking congruence, figures may be rotated or flipped before superimposing. Several pairs of congruent figures are shown to illustrate this. It is emphasized that having the same arm lengths alone does not guarantee congruence; the angle between them must also be the same. This section ends with exercises to identify congruent figures and to consider what measurements are needed to create congruent circles and rectangles.

📊 Diagram: Diagrams include the original symbol on the signboard with points A, B, C marked; multiple symbols with same arm lengths but different angles; pairs of congruent figures shown with tracing paper superimposition; examples of rotated and flipped congruent figures.

🧪 Activity: Exercises to check congruence of given pairs of figures and to identify measurements needed to create congruent circles and rectangles.

🔗 Connection: Leads to the study of congruence in triangles, introducing formal conditions and methods to verify congruence.

Frequently asked questions

ΔABC is isosceles with AB = AC, and ∠A = 80°. What can we say about ∠B and ∠C? Construct the altitude from A to BC. Can you use this fact to find ∠B and ∠C?

Since ΔABC is isosceles with AB = AC, the angles opposite these sides are equal. Constructing the altitude AD from A to BC creates two right triangles, ΔADB and ΔADC. By RHS congruence (Right angle, Hypotenuse, Side), ΔADB ≅ ΔADC. Therefore, ∠B = ∠C. Since the sum of angles in ΔABC is 180°, we have ∠A + ∠B + ∠C = 180°. Given ∠A = 80°, and ∠B = ∠C, let each be x. Then 80° + x + x = 180°, so 2x = 100°, x = 50°. Hence, ∠B = ∠C = 50°.

What can we say about the angles of an equilateral triangle? Verify this by construction. What could be their measures?

In an equilateral triangle, all sides are equal. Using the fact that angles opposite equal sides are equal, all three angles are equal. Since the sum of angles in a triangle is 180°, each angle measures 180° ÷ 3 = 60°. This can be verified by constructing an equilateral triangle and measuring its angles.

1. ΔAIR ≅ ΔFLY. Identify the corresponding vertices, sides and angles. 2. Each of the following cases contains certain measurements taken from two triangles. Identify the pairs in which the triangles are congruent to each other, with reason. Express the congruence whenever they are congruent. (a) AB = DE, BC = EF, CA = DF (b) AB = EF, ∠A = ∠E, AC = ED (c) AB = DF, ∠B = ∠D = 90°, AC = FE (d) ∠A = ∠D, ∠B = ∠E, AC = DF (e) AB = DF, ∠B = ∠F, AC = DE 3. It is given that OB = OC, and OA = OD. Show that AB is parallel to CD. [Hint: AD is a transversal for these two lines. Are there any equal alternate angles?] 4. ABCD is a square. Show that ΔABC ≅ ΔADC. Is ΔABC also congruent to ΔCDA? Give more examples of two triangles where one triangle is congruent to the other in two different ways, as in the case above. Can you give an example of two triangles where one is congruent to the other in six different ways? 5. Find ∠B and ∠C, if A is the centre of the circle. 6. Find the missing angles. As per the convention that we have been following, all line segments marked with a single ‘|’ are equal to each other and those marked with a double ‘|’ are equal to each other, etc.

1. Corresponding vertices: A ↔ F, I ↔ L, R ↔ Y. Corresponding sides: AI ↔ FL, IR ↔ LY, AR ↔ FY. Corresponding angles: ∠A ↔ ∠F, ∠I ↔ ∠L, ∠R ↔ ∠Y.

2. (a) AB=DE, BC=EF, CA=DF → SSS congruence → ΔABC ≅ ΔDEF. (b) AB=EF, ∠A=∠E, AC=ED → SAS congruence → ΔABC ≅ ΔEFD. (c) AB=DF, ∠B=∠D=90°, AC=FE → RHS congruence → ΔABC ≅ ΔDFE. (d) ∠A=∠D, ∠B=∠E, AC=DF → ASA congruence → ΔABC ≅ ΔDEF. (e) AB=DF, ∠B=∠F, AC=DE → Not sufficient for congruence (two angles and non-included side).

3. Given OB=OC and OA=OD, cons

Draw lines and split the region consisting of white squares into 6 smaller congruent regions.

To split the given region of white squares into 6 smaller congruent regions, draw lines such that each smaller region is congruent in shape and size. This can be done by dividing the figure symmetrically, ensuring equal areas and congruent shapes. The exact lines depend on the figure shown, but typically involve drawing lines parallel or at angles that create equal partitions.

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