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 4: The angles in any triangle add to 180o
Triangle interior angles definition - Math Open Reference
• Theorem 5: Two lines are parallel if and only if for any transversal, corresponding angles are equal.
Corresponding Angles definition - Math Open Reference
• *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 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
(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
Khan
More to try at IXL maths