Math Geometry Vocabulary Booklet

Geometry Vocabulary Booklet By Eamon Barkhordarian

May 17, 2006 Acute triangle- a triangle whose interior angles are all acute

Adjacent angle- Either of two angles having a common side and a common vertex Circle- A line or process with every point equidistant from the center Complementary angles- Two angles whose sum is 90° Diameter- A straight line segment passing through the center of a figure, especially of a circle or sphere, and terminating at the periphery Equilateral triangle- A triangle that had all sides of equal length Isosceles triangle- a triangle with two equal sides Obtuse triangle- a triangle that contains an obtuse interior angle Parallelogram- A four-sided plane figure with opposite sides parallel Perpendicular- Intersecting at or forming right angles Quadrilateral- A polygon having four sides Radius- A line segment that joins the center of a circle with any point on its circumference Rectangle- A four-sided plane figure with four right angles

Right triangle- a triangle with one right angle Scalene triangle- a triangle with no two sides of equal length Supplementary angle- The angle or arc that when added to a given angle or arc makes 180° or a semicircle Trapezoid- A quadrilateral having two parallel sides Vertical angle- Either of two angles formed by two intersecting lines and lying on opposite sides of the point of intersection

FORMULAS Area of a circle- r × pi 2

Area of a parallelogram- height × base Area of a triangle- height × base / 2 Circumference of a circle- diameter × pi Volume of a cylinder- area of top × height Volume of a rectangular prism- length × width × height Volume of a triangular prism- 1/2 × length × width × height

Table of Contents Vocabulary words----------------------------------------------------------------1-2 Acute triangle----------------------------------------------------------------------3 Adjacent angle---------------------------------------------------------------------4 Area of a circle--------------------------------------------------------------------21 Area of a parallelogram----------------------------------------------------------21 Area of a triangle------------------------------------------------------------------21 Circle--------------------------------------------------------------------------------5 Circumference of a circle--------------------------------------------------------21 Complementary angles-----------------------------------------------------------6 Diameter----------------------------------------------------------------------------7 Equilateral triangle----------------------------------------------------------------8 Isosceles triangle------------------------------------------------------------------9 Obtuse triangle--------------------------------------------------------------------10 Parallelogram----------------------------------------------------------------------11 Perpendicular----------------------------------------------------------------------12 Quadrilateral-----------------------------------------------------------------------13 Radius------------------------------------------------------------------------------14 Rectangle--------------------------------------------------------------------------15 Right triangle----------------------------------------------------------------------16 Scalene triangle-------------------------------------------------------------------17 Supplementary angle-------------------------------------------------------------18 Trapezoid--------------------------------------------------------------------------19 Vertical angle---------------------------------------------------------------------20 Volume of a cylinder------------------------------------------------------------21 Volume of a rectangular prism-------------------------------------------------21 Volume of a triangular prism---------------------------------------------------21

Acute triangle Acute triangle- a triangle whose interior angles are all acute

An acute triangle is a triangle in which all three angles are acute angles. As you can see, angle A, B, and C are all acute, causing this triangle to be an acute triangle.

All three angles are less than 90 degrees.

Adjacent angles Adjacent angle- Either of two angles having a common side and a common vertex In the diagram, angles 1 and 2 are adjacent angles. So are angles 2 and 3, angles 3 and 4, and angles 4 and 1.

Angle 1 is the same angle as angle 3, as angle 4 is the same angle as angle 2.

Complementary angles Complementary angles- Two angles whose sum is 90° Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. One of the complementary angles is said to be the complement of the other.

Note that these two angles can be "pasted" together to form a right angle.

Then once you “paste” the two angles together, you get a complementary angle.

Diameter Diameter- A straight line connecting two opposite points on the surface of a spherical or cylindrical body. The diameter of a circle is the distance from a point on the circle, to the opposite point.

The diameter is 2x the radius and cuts straight through the circle with a line from one point of the circle, to the opposite point.

Equilateral Triangle Equilateral triangle- A triangle that had all sides of equal length An equilateral triangle also must have all angles the same too, or else it would be impossible to create an equilateral triangle.

As you can see, all the sides are the same, and so are all the angles, making this an equilateral triangle.

Isosceles Triangle Isosceles triangle- a triangle with two equal sides

An isosceles triangle also must have two angles the same, or else it would be impossible to create it.

In the figure above, the two equal sides have length and the remaining side has length . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles.

Obtuse Triangle Obtuse triangle- a triangle that contains an obtuse interior angle “Obtuse” means more than 90 degrees, An obtuse triangle only has one obtuse angle, because it is impossible to create a triangle with two obtuse angles.

The bottom left angle and the top right angle are both acute, though the bottom right angle is obtuse, causing this triangle to be an obtuse triangle.

Parallelogram Parallelogram- A four-sided plane figure with opposite sides parallel A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A parallelogram whose angles are all right angles is called a rectangle.

Shape #1: Opposite sides and angles are equal Shape #2: Diagonals bisect each other at 0 Shape #3: Area of a parallelogram is height x base

Perpendicular Perpendicular- Intersecting at or forming right angles

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle.

In the above figure, the line segment is perpendicular to the line segment . This relationship is commonly denoted with a small square at the vertex where perpendicular objects meet, as shown above.

Quadrilateral Quadrilateral- A polygon having four sides A quadrilateral sometimes is also known as a tetragon or quadrangle. A quadrilateral with two sides parallel is called a trapezoid, whereas a quadrilateral with opposite pairs of sides parallel is called a parallelogram.

These are just some of the many types of quadrilaterals, so be creative and see if you can find other types of quadrilaterals.

Radius Radius- A line segment that joins the center of a circle with any point on its circumference The radius of a circle is the distance from the center of a circle to its perimeter, or from the center of a sphere to its surface. The radius is equal to half the diameter.

A radius starts from the center of the circle, and ends at any point of the perimeter.

Rectangle Rectangle- A four-sided plane figure with four right angles A closed planar quadrilateral with opposite sides of equal lengths and , and with four right angles is a rectangle.

In the figure above, the shape has 4 right angles, showing that this figure is a rectangle.

Right triangle Right triangle- a triangle with one right angle A triangle with an angle of

is a right triangle.

A right triangle can only have 1 right angle, because if you add any more, it would increase the number of sides in the shape, not making it a triangle anymore.

scalene triangle Scalene triangle- a triangle with no two sides of equal length There are three different types of triangles. One is the scalene triangle, while the other two are right triangle and equilateral triangle

You can see that these are all scalene triangles because it has no two sides of equal length.

Supplementary angles Supplementary angle- The angle or arc that when added to a given angle or arc makes 180° or a semicircle These two angles are supplementary.

Note that these two angles can be "pasted" together to form a straight line.

Then one you “paste” the two angles together, you get a supplementary angle.

Trapezoid Trapezoid- A quadrilateral having two parallel sides A trapezoid is a quadrilateral with two sides parallel. The trapezoid is equivalent to the British definition of trapezium.

Side A, and B are parallel, meaning that this shape above is a trapezoid.

Vertical angle Vertical angle- Either of two angles formed by two intersecting lines and lying on opposite sides of the point of intersection For any two lines that meet, such as in the diagram below, angle AEB and angle DEC are called vertical angles. Vertical angles have the same degree measurement. Angle BEC and angle AED are also vertical angles.

The angle of AEB, is the same angle measurement as DEC; and angle DEA is the same angle measurment as CEB

Formulas Area of a circle- r2× pi Area of a parallelogram- height × base Area of a triangle- height × base / 2 Circumference of a circle- diameter × pi Volume of a cylinder- area of top × height Volume of a rectangular prism- length × width × height Volume of a triangular prism- 1/2 × length × width × height