--- title: "Congruent Triangles and the Congruence Conditions" description: "Use SSS, SAS, ASA and RHS to decide whether two triangles are congruent, and write the decision as a short reasoned argument." canonical: https://lightmysky.com/learn/mathematics/congruent-triangles-and-the-congruence-conditions-mt_it8t7mY71J source: https://lightmysky.com/learn/mathematics/congruent-triangles-and-the-congruence-conditions-mt_it8t7mY71J.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Congruent Triangles and the Congruence Conditions Use SSS, SAS, ASA and RHS to decide whether two triangles are congruent, and write the decision as a short reasoned argument. Subject: Mathematics · Area: Geometry · Ages 14 to 15 Page: https://lightmysky.com/learn/mathematics/congruent-triangles-and-the-congruence-conditions-mt_it8t7mY71J ## Ready when they can - Pick the condition that the information in the diagram matches - Explain why two sides and a non-included angle is not enough - Use a congruence argument to justify that two lengths in a diagram are equal ## Lesson: Proving triangles match exactly Read the tick marks before naming a condition. Three matching sides spell SSS. Two sides with the angle between them spell SAS. Two angles with the side between them spell ASA. A right angle with a matching hypotenuse and one side spells RHS. Angles alone only prove similarity, since size stays free. **Example.** Suppose a diagram gives two sides and an angle that sits outside them. The free side can swing into two positions, building two different triangles from the same data. The honest answer is that congruence is not yet shown, so SSA never settles it. A congruence proof is a short chain: state what matches, name the condition, then conclude. Once triangles are proved congruent, every remaining pair follows, so a marked 7 cm side in one is 7 cm in the other. Copy values across by the pairing, reading letter order as you go. **Tip.** Always ask where the known angle sits. Between the known sides means SAS is safe, while outside them means the swing trap is open. One glance at the angle's place saves most wrong answers. **Recap.** Name the match, check the condition, then copy lengths and angles across. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Triangle congruence criteria](https://lightmysky.com/learn/mathematics/triangle-congruence-criteria-mt_167X6Ax8P7) - [Properties of triangles, quadrilaterals and circles](https://lightmysky.com/learn/mathematics/properties-of-triangles-quadrilaterals-and-circles-mt_DNYQLahbfa) ## Opens up - [Exact Values of Sine, Cosine and Tangent](https://lightmysky.com/learn/mathematics/exact-values-of-sine-cosine-and-tangent-mt_SNJEbXYOrR)