Basic Geometry

Vocabulary Review

Plane and Solid Figures

• Plane figure – a plane figure has just 2 dimensions – length and width.

• Solid figure – a solid figure has 3 dimensions – length, width, and height.

Solid Figures

• Face – each flat surface of a solid figure

• Edge – a line segment where 2 faces meet on a solid figure.

• Vertex – “a corner” – where 3 or more edges meet. The plural form of vertex is “vertices.”

Solid Figures

Polygons

• Polygon – a polygon is a closed plane figure made up of line segments. Each line segment is a side.

Polygons – Know Your Prefixes!• “Tri” – means 3 – a triangle has 3

sides.• “Quad” – means 4 – a

quadrilateral has 4 sides.• “Penta” – means 5 – a pentagon

has 5 sides.• “Hexa” – means 6 – a hexagon

has 6 sides.• “Octa” – means 8 – an octagon

has 8 sides.• “Nona” – means 9 – a nonagon

has 9 sides.• “Deca” – means 10 – a decagon

has ten sides.

Points, Lines, Line Segments, and Rays

• Point – an exact location in space.

• Line – a straight path of points that goes on and on in two directions.

• Line segment – a part of a line. It has 2 endpoints.

• Ray – part of a line. It has one endpoint and continues on and on in only one direction.

Angles• Right angle – has a

square corner

• Acute angle – less than a right angle

• Obtuse angle – more than a right angle.

• Straight angle – forms a straight line.

Lines

• Parallel lines – never intersect.

• Intersecting lines – lines that cross through the same point.

• Perpendicular lines – lines that form right angles where they intersect each other.

Triangles

• We learned that there are 2 ways to classify (or group) triangles.

• One way is to classify (or group) triangles by the length of their sides.

• The second way is to classify (or group) them is by their angles.

• Length of sides – Equilateral, isosceles, or scalene.

• By their angles – right, acute, or obtuse.

Equilateral Triangles

• Equilateral triangles – all 3 sides have the same length.

Isosceles Triangle

• Isosceles triangle – 2 of the sides have the same length. You can see that the base (or bottom) of the triangle is shorter than the 2 sides. However, the 2 sides are the same length.

Scalene Triangle

• Scalene triangle – none of the 3 sides are the same length.

Right Triangle

• Right Triangle – 1 angle of the triangle is a right angle.

Acute Triangle

• Acute triangle – all 3 angles of the triangle are acute angles.

• Remember – if all 3 sides are the same length (equilateral), the triangle is automatically an acute triangle!

Obtuse Triangle

• Obtuse triangle – if one of the angles of the triangle makes an obtuse angle, the triangle is an obtuse triangle.

Quadrilaterals

• Quadrilaterals can also be classified (or grouped) by their angles or their pairs of sides!

• Remember , quad means 4! So we are talking about 4 sided figures!

Rectangle

• Rectangle – there are 4 right angles!

Square

• Square – there are 4 right angles and all sides are the same length.

Trapezoid

• Trapezoid – There is only one pair of parallel sides.

Parallelogram

• Parallelogram – opposite sides are parallel.

Rhombus

• Rhombus – opposite sides are parallel AND all 4 sides are the same length.

Circles

• Circles – we learned that circles are different from other plane figures because they have no sides.

• A circles is a closed plane figure made of all the points in the same distance from a point called the center.

Center of the Circle

Radius

• Radius – is any line that segment that connects the center to a point on the circle.

Diameter

• Diameter – is any line segment that connects two points on the circle and passes through the center.

Chord

• Chord – is any line segment that connects two points on a circle.

Circumference of a Circle

• Circumference – the distance around the outside of a circle.

• The circumference of a circle is calculated by multiplying pi (3.14) times the diameter of the circle.

Congruent

• Congruent – same shape, same size.

Slide (Translation)

• Slide (translation) – moves a figure in a straight direction.

Flip (Reflection)

• Flip (reflection) – a figure gives its mirror image.

Turn (Rotation)

• Turn (rotation) – moves a figure around a point.

Symmetry

• Symmetry – when a figure can be folded into two congruent halves. *Means one half can lay perfectly over the other half in an exact match.

line of symmetry

Similar

• Similar – same shape, but may or may not have the same size! *If items are congruent, they are automatically similar. However, just because items are similar, doesn’t mean they are automatically congruent.

Perimeter

• Perimeter – the distance around the outside of a figure.

• Just add the length of all sides together to calculate the perimeter.

• Real world use of perimeter – building a fence.

Area

• Area – the number of square units needed to cover the region inside a figure.

• Multiply the length x width to find the area of a figure.

• Real world use of area – flooring/carpet.

• Remember – use “square” in your answer. 32 sq. in.

Volume

• Volume – the number of CUBIC units needed to fill a solid figure.

• Multiply the length x width x height to calculate the volume.

• Real world of volume – Shopping for refrigerator or freezers. Shipping companies like UPS or FedEx.

• Remember to use “CUBIC” in your answer. 48 cubic inches.