Extracted/adapted from the MultiChoice program Units 24-25.
Area theorems
Before
we can prove the proportionality theorems, we need to make sure that
we know and understand the following two theorems relating to area of
triangles.
Note:
We use the notation DABC = DDEF
to mean the area of DABC is equal to the area
of DDEF, in contrast to the notation DABC
º DDEF for
congruency.
Areas
of triangles on the same base and between the same parallel lines are
equal.
In
the applet, drag or animate point B. What do you notice?
Then
move A and/or C and repeat. What do you notice? Now drag point P ...
Which values are variable and which are constant?
Can you explain the result? |
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If
two triangles have the same height, their areas are in the same ratio
as the lengths of their bases.
In
the applet, drag point B. What do you notice?
Now drag point D. What do you notice?
Move point A and C and repeat … Formulate
a conjecture and prove it algebraically.
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