GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1
Visual Lessons
Think first. Use AI purposefully. Verify always.
MATCH — Same shape. Same size.
Move without stretching
Solid and dashed copies have the same side lengths. Predict how to align them.
FIX — Which measurements fix a copy?
What is still free to move?
AB = 4 cm and BC = 8 cm throughout. The angle changes the shape. Set 80° to recover the source symbol.
TRIPLE — Three sides determine a triangle
Meet at the circle intersections
AB = 6 cm, AE = 4 cm, BE = 8 cm. △ABE ≅ △ABF by SSS.
ORDER — Correspondence carries meaning
Match vertices before writing the order
Correct order: A ↔ X, B ↔ Y, C ↔ Z.
HINGE — Fix the included angle
A fixed hinge versus a change of scale
AB = 6 cm, AC = 5 cm. With ∠A fixed, the triangle is fixed. Changing ∠A changes the third side.
Angles stay equal; corresponding lengths have ratio 1. These copies are congruent.
AMBIGUOUS — A non-included angle can leave two answers
One ray. Two possible third vertices.
PQ = 6 cm; QR = QS = 4 cm; ∠P = 30°.
Measured model lengths: PR ≈ 2.550 cm; PS ≈ 7.842 cm. They are different, so the triangles are not congruent.
The dashed circle is clipped to the viewing window. Both intersections are shown in the combined view.
ANGLE — Two angles and a side
Recover the missing angle
BC = 4 cm. Predict the missing angle before revealing it.
RIGHT — Right angle, hypotenuse, side
Locate the hypotenuse
∠Q = 90°; QR = 4 cm; PR = 5 cm is the hypotenuse. Reflection preserves the triangle.
DEDUCE — Turn congruence into a reason
Prove the equal base angles
Given only: AB = AC and ∠A = 80°. Do not assume a midpoint.
Equal sides lead to equal angles
AB = BC = CA. What can the isosceles result tell us?