GANITA PRAKASH · GRADE 7 · PART II · CHAPTER 1
RIGHT — Right angle, hypotenuse, side
Think first. Use AI purposefully. Verify always.
DISCOVER
Start with a sketch and a prediction.
Which side is opposite the right angle? Can you locate the third vertex from a leg and that hypotenuse?
Try on paper first. Use the model to test your idea before accepting the explanation.
Understand
RHS applies to two right triangles with equal hypotenuses and one equal corresponding leg. The hypotenuse lies opposite 90°. Do not apply RHS without both right angles.
Key Ideas
RHS — right angle + hypotenuse + leg
The longest-looking side is not proof of a hypotenuse. Locate the established right angle.
Visualise
Locate the hypotenuse
∠Q = 90°; QR = 4 cm; PR = 5 cm is the hypotenuse. Reflection preserves the triangle.
Method
Draw the given leg. Construct a perpendicular at its endpoint. Intersect it with a circle from the other endpoint whose radius is the hypotenuse. The reflected intersection is a congruent copy.
Worked Example
Given
∠B = ∠Y = 90°, AC = XZ = 5 cm and BC = YZ = 4 cm.
To Prove
△ABC ≅ △XYZ
Property
RHS: AC and XZ are opposite the right angles.
Proof
- B ↔ Y are right-angle vertices.
- Hypotenuse AC matches XZ and leg BC matches YZ.
- Thus C ↔ Z and A ↔ X.
Result
△ABC ≅ △XYZ by RHS.
AIMS Method
- A — Attempt independently
Sketch and predict before using a criterion. - I — Investigate the idea
Separate given facts from visual assumptions. - M — Make connections
Match vertices, sides and angles consistently. - S — Scrutinise your reasoning
Check each hypothesis and justify the conclusion.
Think first. Use AI purposefully. Verify always.
Focused Practice
Is an equal hypotenuse alone enough to establish congruence of two right triangles?
Check & Feedback
Name the exact given facts, state a valid criterion or explain why none applies, and check the vertex order.
Textbook connection: Ganita Prakash · Grade 7 · Part II · Chapter 1 — Geometric Twins · printed page 16