Twins hiding in a figure
A figure has marks on its sides and angles. Two triangles inside it may be twins. Which condition proves it?
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The rule
To prove two triangles congruent, find three marked facts. Match them to SSS, SAS, ASA, AAS or RHS. The facts must fit one test exactly. In SAS, the angle sits between the two sides. A side that two triangles share counts as an equal pair.
| Mark | Fact |
|---|---|
| Same number of ticks | The sides are equal |
| Same number of arcs | The angles are equal |
| Small square | The angle is 90° |
| Arrows | The lines are parallel |
Two more facts need no tick or arc. Angles that face each other at a crossing are equal. Parallel lines give equal alternate angles. Alternate angles lie between the parallels. They are on opposite sides of the crossing line.