Unit 3: Geometry

Word / Definition
World Tour /
  • this section contains information that students will use as they take an imaginary world tour.

Geometry Template /
  • plastic device with many uses
  • ruler, half circle protractor, full circle protractor, percent circle, pattern block shapes

Point /
  • a location in space
  • you make a dot with your pencil to show where a point is
  • upper case letters are used to name points.

Line Segment /
  • is made up of 2 points and the straight path between them
  • you can use any tool with a straight edge to draw the path between the two points.
  • the two points are called endpoints of the line segment
  • the points are labeled with upper case letters

Straightedge /
  • a strip of wood, plastic, or metal that may be used to draw a straight line.

Ray /
  • a straight path that has a starting point and goes on forever in one direction
  • the end point is always the first letter in the name of the ray

Line /
  • a straight path that goes on forever in both directions

Angle /
  • formed by 2 rays or two line segments that share the same endpoint.
  • the vertex is where the two segments meet
  • the rays or segments are called the sides of the angle
  • when naming an angle the vertex is always in the middle

Right angle /
  • an angle that measures 90 degrees
  • forms the corner of a square
  • a small square is drawn in the vertex of the angle indicating it is a right angle

Acute angle /
  • an angle that measures between 0 degrees and 90 degrees

Obtuse angle /
  • an angle that measures between 90 degrees and 180 degrees

Straight angle /
  • measures 180 degrees

Reflex angle /
  • an angle that measures greater than 180 degrees and less than 360 degrees

Adjacent angles /
  • angles that are next to each other and share a side and common vertex

Opposite or Vertical angles /
  • when two lines intersect each other 4 angles are formed. The angles "opposite" each other are called vertical angles or opposite angles

Polygon /
  • a closed figure that is made up of line segments joined end to end
  • the line segments do not cross
  • can have any number of sides as long as it has three

Regular polygon /
  • a polygon whose sides are all the same length and whose angles are all equal

Convex /
  • all vertices are pushed out

Concave /
  • at least one vertex is pushed in

Triangle /
  • a polygon with three sides and three angles
  • the measure of all the angles equals 180 degrees

Right Triangle /
  • a triangle with one right angle
  • the angle looks like the corner of a square

Equilateral triangle /
  • a triangle with 3 equal side and 3 equal angles
  • it is a regular polygon

Isosceles triangle /
  • at least two sides are the same length
  • an equilateral triangle is also an isosceles triangle
  • can be a right triangle

Scalene triangle /
  • no sides are the same length
  • can be a right triangle

Congruent /
  • a figure that is an exact copy
  • has the same size and shape

Quadrangle /
  • a polygon with 4 sides
  • the measure of the 4 angles equals 360 degrees
  • also called a quadrilateral

Square /
  • a quadrangle with 4 equal sides and 4 right angles
  • also considered a parallelogram, a rectangle, and a rhombus

Rhombus /
  • a parallelogram that has 4 equal sides
  • the angles are not right angles

Rectangle /
  • a parallelogram with 4 right angles
  • opposite sides are equal in length

Parallelogram /
  • a quadrilateral with 2 pairs of parallel sides
  • opposite sides are parallel

Trapezoid /
  • a quadrangle that has only one pair of parallel lines
  • it is not a parallelogram
  • the 4 sides can all be of a different length

Kite /
  • a quadrangle with 2 pair of equal sides
  • the equal sides are next to each other
  • not a parallelogram

Parallel lines /
  • lines or segments on a flat surface that never meet
  • like railroad tracks

Intersect /
  • lines or segments that cross each other

Perpendicular /
  • lines or line segments that cross and form a right angle

Circle /
  • curved line that forms a closed path on a flat circle
  • not a polygon

Center of a circle /
  • all of the points on a circle will be the same distance from the center

Compass /
  • tool used to draw circles

Radius /
  • any line segment that connects the center of the circle with a point on the circle

Diameter /
  • any line segment that passes through the center of the circle and has both of its endpoints on the circle

Concentric /
  • circles with the same center that do not cross

Inscribed Square /
  • a square whose vertices all lie on a circle

Tessellations /
  • a n arrangement of repeated, closed shapes that cover a surface so that no shapes overlap, and there are no gaps between shapes
  • shapes that tessellate-square, equilateral triangle, hexagon.

Notes and Helpful Hints

Topic / Notes
Properties of Polygons / Polygons can have more than one property, in fact they may have many.
For example: a square has 4 right angles, 4 equal sides, is a parallelogram, is a regular polygon, is a quadrilateral.
Parallelograms: / square, rectangle, rhombus
Not parallelograms: / trapezoid, kite
Perimeter: / add up the length of all the sides
*Remember in a regular polygon all the sides are the same length (even if they are not marked on all the sides)
*In a rectangle the opposite sides are equal (don't forget to add all of them up)
Area: / Square and rectangle: length of the base X the height Formula A=b X h
Triangle: length of the base X the height divided by 2 Formula A= b X h divided by 2.
Circle: / *always mark the center of your circle when drawing it with a compass. This way if the compass slips you know where to replace it.
Circle measures 360 degrees
Circumference: (really the perimeter of the circle) Formula: C= 3.14 (pie) X diameter
Angles / Always label with upper case letters with the vertex in the middle.
Look at the angle and ask yourself "What makes sense?" Is the angle smaller or larger than a right angle?
Protractor /
Always estimate before you measure, it will help you make sure you are reading the correct measurement for the angle. Ask yourself what type of angle do I have? (acute, obtuse, right, straight, reflex)
Half-circle: line up one of the sides of the angle with zero making sure the vertex is in the correct spot
Full-circle: line up one of the sides with the zero and read clockwise.
* If the side of the angle is too short to reach edge of the protractor extend it with a straightedge
Pattern Block Angles / Triangle: angles must add up to 180 degrees, in an equilateral triangle all the angles measure 60 degrees
Quadrilateral: angles must add up to 360 degrees
Hexagon: angles measure 120 degrees