CBSE MATHEMATICS • SELECTED CENTRAL & STATE COMPETITIVE EXAMS
AIMSSchool of MathematicsAim through AIMS
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GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1

Practice

Think first. Use AI purposefully. Verify always.

Seven AIMS sprints. Check the exact data and correspondence before answering. Numerical angle answers use degrees; enter the number without a degree symbol.

Sprint 1 — MATCH & correspondence

Progress: 03 checked correctly

Q1. Which change always preserves congruence?
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Q2. If △ABC ≅ △XYZ, which side matches AC?
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Q3. Two circles have radii 4 cm and 4 cm. Are they congruent?
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Sprint 2 — SSS

Progress: 03 checked correctly

Q1. Which lengths form a non-degenerate triangle?
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Q2. Two triangles each have side lengths 4, 6 and 8 cm. Which criterion applies?
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Q3. SSS construction circles intersect on opposite sides of the base. What follows?
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Sprint 3 — SAS / SSA

Progress: 03 checked correctly

Q1. For sides AB and AC, which angle is included?
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Q2. With PQ = 6, QR = 4 and ∠QPR = 30°, how many different third vertices lie on the specified ray?
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Q3. Triangles have the same three angles. Is congruence guaranteed?
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Sprint 4 — ASA / AAS

Progress: 03 checked correctly

Q1. Two angles are 35° and 75°. Find the third angle in degrees.
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Q2. Equal angles A ↔ X, C ↔ Z and equal sides BC ↔ YZ give which original criterion?
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Q3. Two triangles have B = Y = 50°, C = Z = 30° and BC = YZ = 5 cm. Which criterion applies?
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Sprint 5 — RHS

Progress: 03 checked correctly

Q1. If ∠B = 90° in △ABC, which side is the hypotenuse?
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Q2. What additional condition is needed with equal hypotenuses in two right triangles for RHS?
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Q3. Can RHS be applied to triangles without established right angles?
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Sprint 6 — Proof / application

Progress: 03 checked correctly

Q1. AB = AC and ∠A = 80°. Find ∠B in degrees.
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Q2. A is a circle centre and ∠BAC = 120°. Find ∠ABC in degrees.
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Q3. Find each angle of an equilateral triangle in degrees.
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Sprint 7 — Mixed Mastery

Progress: 04 checked correctly

Q1. In a rectangle ABCD with diagonal BD, which order is always valid?
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Q2. How many valid vertex correspondences can two congruent equilateral triangles have?
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Q3. The 5 × 5 board excludes its centre square. How many unit squares are in each of six congruent equal-area pieces?
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Q4. Which is enough to prove that six puzzle pieces are congruent?
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