Mathematics Class 9
Triangles – Congruence Theorems
Decide how many triangles fixed measurements settle, and why some rules fail.
14 lessons · ~97 min total
Track progress — 0 of 14 lessons read 0%
Lessons in this topic
- 0 Start here A roadmap: the rules that fix a triangle, the one that fails, and what follows from them. · 4 min You are here
- 1 SAS: two sides and the angle between SAS: two sides and the angle between them fix exactly one triangle. · 8 min
- 2 SSA can give two triangles SSA: two sides and an angle not between them can build two different triangles. · 9 min
- 3 RHS: a right angle, the hypotenuse, a leg RHS: a right angle, the hypotenuse and one leg fix exactly one triangle. · 8 min
- 4 AAS: two angles and any side AAS: two angles and a side that is not between them fix one triangle. · 7 min
- 5 Equal sides give equal base angles In an isosceles triangle, the two angles opposite the equal sides are equal. · 8 min
- 6 Checkpoint: SAS, SSA, RHS and AAS A graded check on the first five ideas: SAS, SSA, RHS, AAS and the isosceles result. · 5 min
- 7 Equal angles give equal sides The converse: if two angles of a triangle are equal, the sides opposite them are equal. · 8 min
- 8 One counter-example ends a claim A counter-example is one case where a claim fails. It ends a claim that says always. · 7 min
- 9 Matching parts decide congruence Two triangles are congruent when every matching side and angle is equal. · 7 min
- 10 The apex bisector does three jobs In an isosceles triangle, the apex bisector halves the base and meets it at 90°. · 8 min
- 11 Checkpoint: converse, counter-example and bisector A graded check on the second half: the converse, counter-examples, matching parts and the bisector. · 5 min
- 12 The big picture Nine ideas about triangles, tied back together around one question: how many triangles fit? · 5 min
- 13 Track quiz A cheat-sheet table and a quiz, one question for each of the nine ideas. · 8 min
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