Download 4-5 Isoceles Triangles and corollary

Isosceles Triangles
&
Corollaries
Get:
♥ a piece of patty paper
♥ a straight edge
♥ your pencil
♥ your compass
♥ a protractor
We are going to create an
isosceles triangle with 2
congruent sides.
Isosceles Triangles
♥ Has at least 2 congruent sides.
♥ The angles opposite the congruent
sides are congruent
♥ Converse is also true. The sides
opposite the congruent angles are
also congruent.
♥ This is a COROLLARY.
A corollary naturally follows a
theorem or postulate. We can
prove it if we need to, but it really
makes a lot of sense.
♥ The bisector of the vertex angle of an
isosceles Δ is the perpendicular bisector of
the base.
Vertex angle
Base
In addition, you just learned
that the angles opposite
congruent sides are
congruent…
Equilateral Triangle
♥ An Equilateral triangle is a special case of an Isosceles
Triangle.
♥ Remember that an Isosceles Triangle has AT LEAST 2
congruent sides.
♥ An Equilateral Triangle is also Equiangular.
♥ The bisector of any angle is the
perpendicular bisector of the opposite side.
Let’s
Practice
Find the
measures of:
mFC =
4
mFG =
4
mCG =
4
m<C =
60◦
m<G =
60◦
m<F =
60◦
m<A =
70◦
m<E =
70◦
y=
50 ◦
Complete each statement.
Explain why it is true.
EAB  ?
BCD  ?  DBC
FG  ?  DF
Determine the measure of the indicated angle.
ACB
DCE
BCD
Find the value of x and y.
An exterior angle of an isosceles triangle
has a measure 140.
Find two possible sets of measures for the
angles of the triangle.
Your
assignment
4.5 Practice Worksheet