Proof using congruent triangles
Many tangent results are proved by showing two triangles are congruent.
Practice This ConceptMain explanation
Teacher explanation
Circle proofs often become simple once you spot two triangles with equal sides and a common side or right angle. In tangents, the radii to the points of contact are equal, the tangent-radii angles are right angles, and this often helps prove triangle congruence. Then equal tangent lengths or other results follow.
Example
In triangles OAP and OBP, if OA = OB and OP is common, triangle congruence can help prove PA = PB.
Simple analogy
Equal parts first, congruence next, result after that.
Common confusion
Students sometimes try to prove tangent results by comparing only one side or one angle. A full congruence argument needs enough matching parts.
Exam tip
Look for equal radii, common side, and right angles. These are the usual clues for triangle congruence in circle proofs.
Answer writing and exam use
1-mark use
Write the exact meaning of proof using congruent triangles in one clean line.
2-mark use
Define proof using congruent triangles and add one example or condition.
3-mark use
Explain proof using congruent triangles, show the method or example, and mention the common mistake.
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