Chapter 7, Congruence of Triangles (त्रिभुजों की सर्वांगसमता), deals with the conditions under which two geometric figures (specifically triangles) are exactly the same size and shape.
Table of Contents
Note: The rationalized syllabus focuses heavily on the four main criteria.
Exercise 7.1: Congruence Criteria
This exercise applies the four criteria for proving triangle congruence.
| Q. No. | Type | Example/Condition | Key Concept |
| 1 | Naming Criterion | $\triangle ABC \cong \triangle PQR$ given $AB=PQ$, $BC=QR$, $AC=PR$. Criterion used: SSS (Side-Side-Side) | SSS: If three sides of one triangle are equal to the three corresponding sides of another triangle. |
| 2 | Naming Criterion | $\triangle ABC \cong \triangle XYZ$ given $\angle B = \angle Y$, $AB=XY$, $BC=YZ$. Criterion used: SAS (Side-Angle-Side) | SAS: If two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of another triangle. |
| 3 | Naming Criterion | $\triangle DEF \cong \triangle JKL$ given $\angle D = \angle J$, $\angle F = \angle L$, $DF=JL$. Criterion used: ASA (Angle-Side-Angle) | ASA: If two angles and the included side of one triangle are equal to the corresponding parts of another triangle. |
| 4 | Naming Criterion | $\triangle PQR \cong \triangle XYZ$ where $\angle Q = \angle Y = 90^\circ$, $PR=XZ$, $QR=YZ$. Criterion used: RHS (Right Angle-Hypotenuse-Side) | RHS: In two right triangles, if the hypotenuse and one leg of one triangle are equal to the corresponding hypotenuse and leg of the other triangle. |
| 5 | Correspondence | If $\triangle DEF \cong \triangle BCA$, write the part of $\triangle BCA$ that corresponds to (a) $DF$ and (b) $\angle E$. (a) $DF$ corresponds to $BA$. (b) $\angle E$ corresponds to $\angle C$ |