Triangle Congruence: RHS (Motivate) MCQs Quiz | Class 9

Class IX Mathematics (Code 041), Unit IV: Geometry. This quiz covers the topic Triangle Congruence: RHS (Motivate), focusing on right triangles and the hypotenuse-side condition. Attempt these 10 MCQs to test your understanding, then submit to check your score and download the answer PDF.

Understanding RHS Congruence

The RHS congruence criterion stands for Right angle – Hypotenuse – Side. It is a special congruence condition applicable only to right-angled triangles. Unlike other criteria like SAS or ASA, RHS allows us to prove congruence using a side and the hypotenuse, even though the right angle is not included between them.

Key Conditions for RHS

Two right-angled triangles are congruent if the following three parts of one triangle are equal to the corresponding three parts of the other triangle:

  • Right Angle: Both triangles must have one angle equal to 90 degrees.
  • Hypotenuse: The longest side opposite to the right angle must be equal in both triangles.
  • Side: One of the remaining two sides (legs) must be equal.

Why RHS works

Generally, Side-Side-Angle (SSA) is not a valid congruence criterion because it can lead to ambiguity. However, when the angle is a right angle (90 degrees), the ambiguity disappears, making RHS a valid and powerful tool in geometry.

Comparison Table: RHS vs SAS

Feature RHS Criterion SAS Criterion
Angle Type Must be 90 degrees (Right Angle) Can be any angle
Sides Involved Hypotenuse and one leg Any two sides
Angle Position Not included between sides Must be included between the two sides

Quick Revision Points

  • RHS is strictly for right-angled triangles.
  • If the hypotenuse is not known to be equal, you cannot use RHS (you might use SAS or ASA instead).
  • The “Side” in RHS can be either the base or the perpendicular (altitude).
  • Always check for the right angle first before applying this rule.

Extra Practice Questions

  1. In triangle ABC (angle B = 90) and triangle PQR (angle Q = 90), if AC = PR and AB = PQ, prove they are congruent.
  2. Can we use RHS if we only know that two sides are equal but not the hypotenuse?
  3. Why is the hypotenuse always the longest side in a right triangle?
  4. If hypotenuse and an acute angle are equal, which criterion is used (RHS or AAS)?
  5. Draw two right triangles that satisfy the RHS condition.