1. Grade 10 Academic (MPM2D) Unit 2: Analytic Geometry Properties of Triangles and Quadrilaterals
Mr. Choi
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2. Properties of Triangles
Pythagorean Theorem
used to find the length of sides of a right triangle
Properties of Triangles and Quadrilaterals
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3. Types of Triangles Properties of Triangles and Quadrilaterals
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4. Some Triangles Theorems Sum of Angles in a Triangle Theorem (SATT)
Properties of Triangles and Quadrilaterals
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5. Some Triangles Theorems Exterior Angle Theorem (EAT)
Properties of Triangles and Quadrilaterals
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6. Some Triangles Theorems Isosceles Triangle Theorem (ITT)
Properties of Triangles and Quadrilaterals
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7. Some Angles Theorems Complementary Angles (CA)
Properties of Triangles and Quadrilaterals
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8. Some Angles Theorems Supplementary Angles (SA)
Properties of Triangles and Quadrilaterals
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9. Some Angles Theorems Opposite Angle Theorem(OAT)
Properties of Triangles and Quadrilaterals
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10. Some Angles Theorems Sum of Angles in a Triangle Theorem(SATT)
Properties of Triangles and Quadrilaterals
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11. Parallel Lines Theorems Alternate Angles (PLT-Z)
Properties of Triangles and Quadrilaterals
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12. Parallel Lines Theorems Corresponding Angles (PLT-F)
Properties of Triangles and Quadrilaterals
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13. Parallel Lines Theorems Interior Angles (PLT-C)
Properties of Triangles and Quadrilaterals
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14. Properties of Triangles
Medians:
line from vertex to the midpoint of the opposite side
Midpoint:
point on a line that divides it into 2 equal parts
to draw a median  find mid point of opposite side and connect to vertex
Altitude:
shows the height of a polygon
to draw an altitude  line from vertex to opposite side so that it meets at 90°
Perpendicular bisectors:
perpendicular to a line segment and meets at its midpoint.
to draw a perpendicular bisector  find midpoint, then measure a right angle, draw line.
Angle bisectors:
The (interior) bisector of an angle, also called the internal angle bisector is the line or line segment that divides the angle into two equal parts 
Centroid:
where all 3 medians meet
divides each median in the ratio 1: 2
it is the centre of mass
Orthocentre:
where all 3 altitudes meet
Circumcentre:
where all 3 perpendicular bisectors meet centre of the circle that passes through the vertices of the triangle
the circle is called circumcircle or circumscribed circle
Incentre:
where all 3 angle bisectors meet centre of the circle that meets each side once
the circle is called incircle or inscribed circle
Properties of Triangles and Quadrilaterals
© 2017 E. Choi – MPM2D - All Rights Reserved

15. Median & Centroid Medians:
line from vertex to the midpoint of the opposite side
Centroid:
where all 3 medians meet
divides each median in the ratio 1: 2
it is the centre of mass
Properties of Triangles and Quadrilaterals
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16. Altitude & Orthocentre
shows the height of a polygon
to draw an altitude  line from vertex to opposite side so that it meets at 90°
Orthocentre:
where all 3 altitudes meet
Properties of Triangles and Quadrilaterals
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17. Perpendicular Bisector & Circumcentre
Perpendicular bisectors:
perpendicular to a line segment and meets at its midpoint.
to draw a perpendicular bisector  find midpoint, then measure a right angle, draw line.
Circumcentre:
where all 3 perpendicular bisectors meet centre of the circle that passes through the vertices of the triangle
the circle is called circumcircle or circumscribed circle
Properties of Triangles and Quadrilaterals
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18. Angle Bisector & Incentre
Angle bisectors:
The (interior) bisector of an angle, also called the internal angle bisector is the line or line segment that divides the angle into two equal parts 
Incentre:
where all 3 angle bisectors meet centre of the circle that meets each side once the circle is called incircle or inscribed circle
Properties of Triangles and Quadrilaterals
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19. Properties of Quadrilaterals
What is a quadrilateral?
Polygon with 4 sides and sum of the angles is 360o
Properties of Triangles and Quadrilaterals
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20. Properties of Quadrilaterals
Picture
Description & Properties
Square
Quadrilateral with 4 sides are equal
All angles are 90o
Diagonals are perpendicular to each other
Rectangle
Quadrilateral with 2 pairs of equal opposite sides
Diagonals are not perpendicular to each other
Properties of Triangles and Quadrilaterals
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21. Properties of Quadrilaterals
Picture
Description & Properties
Rhombus
Quadrilateral with 4 sides are equal
None of angles is 90o
A pair of acute angles and a pair of obtuse angles
Diagonals are perpendicular to each other
Parallelogram
Quadrilateral with 2 pairs of equal opposite sides
Diagonals are not perpendicular to each other
Properties of Triangles and Quadrilaterals
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22. Properties of Quadrilaterals
Picture
Description & Properties
Kite
Quadrilateral with 2 pairs of equal adjacent sides
Diagonals are perpendicular to each other
Trapezoid
Quadrilateral with 1 pair of unequal but parallel opposite sides
Properties of Triangles and Quadrilaterals
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23. Homework Work sheet: Cartesian Triangles - A Summary Text:
Read P. 33 & 38. Make Summary notes
P. 34    #1 - 4
P. 39    #1, 2, 4, 5, 6
Read P. 36. Make Summary notes
P. 37    #1, 2, 3, 4, 6, 7
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Properties of Triangles and Quadrilaterals
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24. End of lesson Properties of Triangles and Quadrilaterals
© 2017 E. Choi – MPM2D - All Rights Reserved