Download PP Section 5.4

Geometry Section 5.4
Equilateral & Isosceles Triangles
What you will learn:
1. Use the Base Angles Theorem and Its
Converse
2. Use Isosceles and Equilateral triangles
2 congruent sides
legs
base
angle
angles
vertex
base
Theorem 5.6 Base Angles Theorem
If two sides of a triangle are congruent, then the
angles opposite them are congruent.
Theorem 5.6 Converse of Base Angles Theorem
If two angles of a triangle are congruent, then the sides
opposite them are congruent.
180  38  142
142  2  71
64
64
64  64  2 x  11  180
2 x  117  180
2 x  63
x  31.5
71 71
180  71  109
180  3  60
3 x  6  5 x  15
6 x  11  8 x  12
23  2 x
x  11.5
21  2 x
x  10.5
B
acute isosceles
45
A
67.5
67.5
180  45  135
135  2  67.5
C
Corollary 5.2: Corollary to the Base Angles Theorem
If a triangle is equilateral, then it is equiangular.
Corollary 5.3: Corollary to the Converse of the Base
Angles Theorem
If a triangle is equiangular, then it is equilateral.
Constructing an equilateral triangle
This construction will be particularly important for
us because it gives us a 60o angle.
Note that KLN is equiagular
and thus equilateral
y  4 and NL  4
Since LNM  LMN, LN  LM
x 1  4
x 3
HW: pp256 & 257 / 3-11, 13-17, 22-24, 31