MPM2D
Lesson 01
Geometric Properties
VERIFYING TRIANGLES
LEARNING GOALS
Students will:

Verify triangle properties using slope, midpoint, and length formulas.
VOCABULARY
Collinear: lying on the same line.
Centroid: the point where the three medians intersect.
INVESTIGATE
EXAMPLE 1: MEDIAN OF AN ISOSCELES TRIANGLE AND ITS PROPERTIES
In the space below sketch triangle ABC, where A (-4, 0), B (4, 0) and C (0, 6).
A. What type of triangle did you draw?
_________________
B. Verify the shape of the triangle using
analytic geometry
C. Draw an altitude from point C and name it point D (where it intersects line AB). What
other name can you call this altitude?
D. Find the area of triangle ABC and of triangle ADC, what do you notice?
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MPM2D
Lesson 01
Geometric Properties
EXAMPLE 2: MIDPOINTS OF THE SIDES OF A TRIANGLE
Sketch triangle ABC on the graph below, where A (1, 3), B (5, 1) and C (7, 5).
A. Find point D (the midpoint of side AC) and label on
the triangle.
B. Find point E (the midpoint of side BC) and label it on
the triangle above
C. Verify that line segment DE is parallel to side AB
D. Verify that line segment DE is half the length of side AB
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MPM2D
Lesson 01
Geometric Properties
EXAMPLE 3: CENTROID OF A TRIANGLE
In the space below sketch triangle OPQ, where O (0, 0), Q (4, 4) and Q (8, -4)
A. Find the equation of median O
B. Find the equation of median Q
C. Using both medians find the centroid. Label the centroid as point C on the graph above.
D. b. Verify that the centroid divides each median in a 2:1 ratio. Note: Find the length of
either median O or Q and compare that to the length of the OC or QC.
HOMEFUN 
Pg. 124 #2abc,3,4,15
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