LCHL Revision of JC synthetic geometry - Theorems 3, 4, 5, 6, 7 & 8

These lessons will involve the students in investigating and understanding:

• Theorem 3: (i) If a transversal makes equal alternate angles on two lines, then the lines are parallel.

(ii) Conversely, if two lines are parallel, then any transversal will make equal alternate angles with them.

Alternate Interior Angles definition - Math Open Reference

Theorem 3

• *Theorem 4: The angles in any triangle add to 180^o

Triangle interior angles definition - Math Open Reference

Theorem 4

Theorem 4 (HL)

• Theorem 5: Two lines are parallel if and only if for any transversal, corresponding angles are equal.

Corresponding Angles definition - Math Open Reference

Theorem 5

• *Theorem 6: Each exterior angle of a triangle is equal to the sum of the interior opposite angles. Page 40 of 104

Triangle exterior angle theorem - Math Open Reference

Triangle exterior angles definition - Math Open Reference

Theorem 6

Theorem 6 (HL)

• Theorem 7: The angle opposite the greater of two sides is greater than the angle opposite the lesser. Conversely, the side opposite the greater of two angles is greater than the side opposite the lesser angle.

Relationship of side lengths and angles of a triangle - Math Open Reference

Theorem 7

(Students might engage with proof by contradiction in proving the converse ot Theorem 7)

• Theorem 8: Two sides of a triangle are together greater than the third.

Triangle inequality theorem- Math Open Reference

Theorem 8

Khan

Triangle inequality theorem

More to try at IXL maths

V.4Angle-side relationships in triangles

V.5Triangle Inequality Theorem