Download Triangle

Geometry Vocabulary
• Triangle: a polygon with three sides.
Sum of the interior
angles of a triangle =
180⁰
• Acute Triangle: a triangle in which all of the
angles are less than 90⁰.
• Obtuse Triangles: A triangle with one angle
that measures more than 90⁰.
• Similar Triangles: Triangles with congruent
angles and proportional sides.
Proportional: Two
variables which
have a constant ratio
between them.
• Right Triangle: A triangle that has one angle
that equals 90⁰.
– Hypotenuse: the longest side of a right triangle
only. It is also the side directly across from the
right angle.
– Legs: the sides of a right triangle that form the
right angle.
hypotenuse
Leg
Leg
Leg
Leg
• 30-60-90 Triangle: In this triangle, the
hypotenuse is twice the shorter leg and the
longer leg is equal to the shorter leg time √3.
• 45-45-90 Triangle: In this triangle, the
hypotenuse is equal to the leg multiplied
by √2.
• Equilateral Triangle: This is a triangle with all
sides equal in length.
• Equiangular Triangle: A triangle with all
congruent angles.
• Isosceles: This is a triangle with at least two
congruent sides.
• Scalene: This is a triangle with three unequal
sides.
– The mathematical relationship relating the three
sides of a right triangle .
2
a
+
2
b
=
2
c
Pythagorean Triple: A set of 3 nonzero whole
numbers that form the sides of a right triangle.
(i.e. these numbers satisfy the formula a2 + b2 = c2)
• Pythagorean Theorem Converse: If the square
of the length of the longest side of the triangle
is equal to the sum of the squares of the
lengths of the other two sides, then the
triangle is a right triangle.
9 + 16 = 25
• Polygon: A closed plane figure formed by
three or more line segments that do not cross
over each other.
• Regular Polygon: A convex polygon with
congruent angles and congruent sides.
Concave
means
CAVED-in.
Convex
means
curved-out.
• Quadrilateral: A polygon with 4
sides. (i.e. square or rectangle)
• Cone: This is a shape whose base is
a circle and whose sides taper up to
a point.
• Cylinder: This is a solid bounded by a
curved lateral surface and two
circular bases.
• Pyramid: This is a polyhedron having
a polygon for a base and triangular
sides with a common vertex.
• Prism: This is a solid with two parallel and
congruent bases in the shape of polygons; the
other faces are parallelograms.
• Rectangular Prism: This is a solid figure where
all sides are rectangles and all sides meet at
right angles.
• Sphere: This is a round shell
defined by a center point
and a surface that lies at a
constant distance from its
center.
• Three-Dimensional Sphere:
A three dimension solid that
consists of all points
equidistant from a given
point.
• Angle: These are two rays sharing a
common endpoint. They are typically
measured in degrees or radians.
• Vertex: The point where the edges of a
three dimensional figure intersect. (Also:
A vertex is the maximum or minimum of
a parabola, depending on whether the
parabola opens up or down.)
• Adjacent Angles: These are two angles in a
plane which share a common vertex and a
common side but do not overlap.
• Corresponding Angles: These are two angles
that are formed by two coplanar lines and a
transversal. They occupy the same relative
positions.
• Supplementary Angles: Two angles whose
measure add up to 180 degrees.
• Complementary Angles: These are a pair of
angles, adjacent or nonadjacent, whose sum is
90 degrees.
• Vertical Angles: These are angles opposite
one another at the intersection of two lines.
• Congruent: These are angles, segments,
triangles, etc. that have exactly the same
measures.
• Face: One of the polygons that makes up
a geometric solid.
• Edge: The segment formed by the
intersection of two faces in a geometric
solid.
• Net: A 2-dimensional representation of a
3-dimensional figure.
(Illustration on next slide)
Edge
Face
• Sum of Interior Angles of a Polygon: This sum
is found by subtracting 2 from the number of
sides and then multiplying by 180⁰.
m = 180⁰ (n – 2)
Where:
m = the measure of the
sum of the interior angles
and
n = the number of sides of
the polygon