Download Applied Geometry

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Tessellation wikipedia, lookup

Multilateration wikipedia, lookup

Steinitz's theorem wikipedia, lookup

Simplex wikipedia, lookup

Golden ratio wikipedia, lookup

History of geometry wikipedia, lookup

Euler angles wikipedia, lookup

Noether's theorem wikipedia, lookup

Riemann–Roch theorem wikipedia, lookup

Brouwer fixed-point theorem wikipedia, lookup

Four color theorem wikipedia, lookup

Reuleaux triangle wikipedia, lookup

Rational trigonometry wikipedia, lookup

Trigonometric functions wikipedia, lookup

History of trigonometry wikipedia, lookup

Incircle and excircles of a triangle wikipedia, lookup

Euclidean geometry wikipedia, lookup

Integer triangle wikipedia, lookup

Pythagorean theorem wikipedia, lookup

Transcript
Applied Geometry
Lesson: 6 – 4
Isosceles Triangles
Objective:
Learn to identify and use properties of isosceles triangles.
Parts of an Isosceles
Triangle
Isosceles Triangle
Theorem
If two sides of a triangle are congruent,
then the angles opposite the sides are
congruent.
Theorem 6-3
The median from the vertex angle of an
isosceles triangle lies on the
perpendicular bisector of the base and the
angle bisector of the vertex angle.
x = 49
y = 90
Because EG is also
a perpendicular bisector.
x = 65
y = 50
x = 90
y = 70
Converse of Isosceles
Triangle Theorem
If two angles of a triangle are congruent,
then the sides opposite those angles
are congruent.
mB  48
mA  mB  mC  180
48  48  mC  180
mC  84
4x = 6x - 5 AC = 4(2.5) = 10
-2x = -5
x = 2.5
BC = 6(2.5) -5 = 10
mC  84
AC  10
BC  10
Theorem 6-5
A triangle is equilateral if and only if it is
equiangular.
Homework
Pg. 249 1 – 5 all, 6 – 22 E