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P. 50
Similarity
are the new triangles still similar?
Justify your answer.
16. A teacher at Magoda Secondary
School has tasked Adolfina with
finding the height of a tall tree
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in front of the office. Using the
Mathematics for Secondary Schools 12. It is given that ΔUVW and ΔUXY you advise Adolfina to accomplish
knowledge of similarity, how would
ˆ
ˆ
are similar with UXY = WVX and
this task?
WY = VW. Find the value of y.
Similarity theorems
Similarly theorems are used to solve
problems based on similar triangles.
If ABC∆ ∆ XYZ,it means;
(a) Corresponding angles are
ˆ
ˆ
equal. That is ABC=XYZ,
ˆ
ˆ
ˆ
ˆ
CAB=ZXY, and BCA=YZX.
(b) The ratio of corresponding sides
13. In the following figure, find the
value of x. is equal. That is, AB = BC = AC .
XY YZ XZ
Note
The value of the constant ratio obtained
from the ratio of corresponding sides of
similar figures is called the constant of
proportionality or scale factor.
To prove similarity of two triangles,
only one of the following conditions is
sufficient.
14. Show that the perimeters of similar 1. Two pairs of corresponding angles are
triangles have the same ratio as equal. This introduces an Angle-Angle
their corresponding sides. (AA) similarity theorem.
15. If k units are added to the length of
each side of two similar triangles, 2. Three corresponding sides are
proportional. This is described by
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Student's Book Form Two
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MATHEMATIC F2 v5.indd 44
