Download 1 Geometry Notes 1-4 Essentials of Geometry Triangles Polygon: A

Geometry
Notes 1-4
Essentials of Geometry
Triangles
Polygon: A closed figure in a plane that is the union of line segments such that
the segments intersect only at their endpoints and no segments sharing a
common endpoint are collinear.
Triangle: A polygon that has exactly 3 sides.
1.
2.
3.
4.
5.
6.
Included sides and Included Angles of a Triangle
AB is included between <A and <B
C
BC is included between <B and <C
CA is included between <C and <A
<A is included between AB and AC
<B is included between BA and BC
B
A
<C is included between CA and CB
Scalene Triangle: A triangle that has no congruent sides.
scalene
Isosceles Triangle: A triangle that has 2 congruent sides.
Equilateral Triangle: A triangle that has three congruent sides.
equilateral
isosceles
The Isosceles Triangle
vertex
angle
Legs: the two congruent sides
Base: the third side, not a leg
Base Angle: angle whose vertices are on the base of
the triangle; they are opposite the legs and are
congruent.
leg
leg
Vertex Angle: angle formed by the two congruent sides
base
angle
base
angle
base
1
Classifying Triangles According to Angles
Acute Triangle: A triangle that has three acute angles.
Right Triangle: A triangle that has a right angle.
Obtuse Triangle: A triangle that has an obtuse angle.
Equiangular Triangle: A triangle that has three congruent angles.
Right Triangle
Legs: the two sides of the right triangle
that form the right angle
hy
p
leg
ot
en
us
e
Hypotenuse: the side across from the right angle;
it is the longest side of the right triangle
leg
Examples:
1. The lengths of the sides of an equilateral triangle are 3x + 1, 5x - 9, and 2y + 2.
a. What are the lengths of the sides of the triangle?
b. What is the value of y?
2. The length of the legs of an isosceles triangle are 2x - 10 and x + 4. What are the
lengths of the legs of the triangle?
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