MPM2D1 Unit 7 Lesson 1
7.1: Similar Triangles
DEFINITIONS:
Similar Figures have the same shape, but not necessarily the same size
(i.e. architects use similar figures when they create scale models of buildings)
Likewise, Similar Triangles have the same shape, but not necessarily the same size.
Example 1: ΔABC ~ ΔDEF (Note: The symbol ‘ ~’ means similar)
PROPERTIES OF SIMILAR TRIANGLESFor similar triangles / For example 1, since ΔABC ~ ΔDEF then:
1. The corresponding angles are equal /
2. The ratios of the corresponding sides are equal /
3. The ratio of their areas is equal to the ratio of the squares of their corresponding sides /
Example 2: Show that ΔPQR ~ ΔTSR given that PQ is parallel to ST.
// PLT – Z
PLT – Z
OAT
Since all corresponding angles are equal, the 2 triangles are similar.
Example 3: ΔBCD and ΔEFG are similar.
a) Find the values of b and g.
b) If the area of ΔBCD is 49 cm2, then determine the area of ΔEFG.
a)
63 = 21g
g=3 / and /
9b = 252
b = 28
b) OR OR
441x = 49 (81)
441x = 3969
441 441
x = 9
The area of ΔEFG is 9 cm2.
Example 3: The diagram below shows how surveyors can lay out two right angle triangles to find the width of a river. Use the triangles to calculate DE, the width of the river.
/ Since the triangles are similar, the ratios of the corresponding sides are equal.20 (DE) = 1200
DE = 60
The width of the river is 60 m.
Therefore, similar triangles can be used to find large inaccessible distances.
How can we use similar triangles to calculate the height of the CN Tower or even the flag pole in front of St. Marguerite d’Youville?
HOMEWORK: Pg. 333-334 #1-4, (6-9)a Section 7.1
Pg. 347-348 #1,5, (6-8)ab, 9-11 Section 7.2
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