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MPM 2D - A Mathematical Verification (Proof) 3 steps: Statement: what are the properties that you going to prove in order to verify the claim? Ie. Verify the properties of a parallelogram ABCD Prove: opposite slopes are equal π¦ −π¦ Solve: ππ΄πΆ = π₯2 −π₯1 , ππ΅π· =, 2 Conclude: 1 ππ΄π΅ =, ππ΄πΆ = ππ΅π· πππ ππ΄π΅ = ππΆπ· ππΆπ· = ∴ The shape is a parallelogram because 2 pairs of opposite sides have equal slopes so they are parallel FOR THESE OTHER QUADRILATERALS: Rectangle: prove it is a parallelogram PLUS adjacent sides are perpendicular Use slope equation as above PLUS show that adjacent sides are negative reciprocals Square: prove it is a rectangle PLUS all sides are equal length Use slope equation as above PLUS ππ΄π΅ = √(π₯2 − π₯1 )2 + (π¦2 − π¦1 )2 πππ πππ π ππππ Rhombus: prove 2 pairs of opposite sides are parallel PLUS all sides are equal length FOR TRIANGLE properties: SCALENE: prove all side lengths are not equal Use distance equation ππ΄π΅ = √(π₯2 − π₯1 )2 + (π¦2 − π¦1 )2 πππ πππ π ππππ Isosceles: prove 2 sides are equal, one different Use distance equation ππ΄π΅ = √(π₯2 − π₯1 )2 + (π¦2 − π¦1 )2 πππ πππ π ππππ Equilateral: prove 3 sides are equal Use distance equation ππ΄π΅ = √(π₯2 − π₯1 )2 + (π¦2 − π¦1 )2 πππ πππ π ππππ Right-angled: prove one 2 slopes are negative reciprocals of each other Use slope equation ππ΄π΅ = π¦2 −π¦1 π₯2 −π₯1 Solving Word Problems 4 steps: Identify what the problem is asking you to solve. Sketch the situation. Plan the steps you will need to solve. Write a concluding statement that answers the question. Pay attention to any units that may be involved.