LCHL Revision of JC synthetic geometry - Constructions 6,7,10,11,12, Axiom 4, Theorem 2

These lessons will involve the students in investigating and understanding:

• Construction 6: Division of a line segment into 2, 3 equal segments without measuring it

• Construction 7: Division of a line segment into any number of equal segments, without measuring it

Revision of and Congruent triangles

• Construction 10: Triangle given SSS data (Axiom 4 -Congruent triangles)

• Construction 11: Triangle given SAS data (Axiom 4 -Congruent triangles)

• Construction 12: Triangle given ASA data (Axiom 4 -Congruent triangles)

• More constructions of triangles with SSS, SAS and ASA

• By construction, show that AAA and AAS are not sufficient conditions for congruence.

• Theorem 2: (i) In an isosceles triangle the angles opposite the equal sides are equal.

• What is meant by the term “converse"

• (ii) Conversely, if two angles are equal, then the triangle is isosceles

Khan