M4.4.4 For the adult

Congruent triangles

Two triangles have two equal sides and one equal angle. Must they be exactly the same?

What this chapter teaches

Congruent triangles are exactly the same size and form. Three facts in the right pattern prove it: three sides (SSS), two sides and the angle between them (SAS), two angles and a side (ASA), or a right angle, the hypotenuse and one side (RHS). Two sides and an angle not between them (SSA) does not prove congruence in general, because two different triangles can fit the facts. RHS works because the angle is 90°.

Three questions to ask

There is no one right wording. Listen for the idea.

  1. Which patterns of three facts show two triangles are congruent?
  2. Why does the equal angle have to be between the two equal sides for SAS?
  3. How do congruent triangles show that the base angles of an isosceles triangle are equal?

After the chapter, the learner can

  • Show two triangles are congruent using SSS, SAS, ASA or RHS
  • Use congruent triangles to prove a simple fact

What they copy into their notebook

Congruent triangles match exactly. Tests: SSS, SAS (angle between), ASA, RHS. SSA is not a test, but RHS works. Use them to prove things, such as equal base angles.

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