2d Shapes

Plane Geometry is the study of flat shapes that you see in pictures or on paper. These shapes include lines, circles, triangles, squares, and rectangles. They are called flat because they have only length and width.

A side is a straight line on a shape.

A vertex is a point where two sides meet.

A circle is every point on the edge as same distance from the center.
The radius is a line segment from the center to a point of the circle. The radius is also the length of this segment.
The diameter is a line segment that goes across the circle through the center, connecting two points on the circle. The diameter is also the length of this segment.

• The diameter is twice the radius: \(\textcolor{colorprop}{d}=2\times \textcolor{colordef}{r}\).
• The radius is half the diameter: \(\textcolor{colordef}{r}=\textcolor{colorprop}{d} \div 2\)

To construct a circle with a radius of 3 cm at center \(O\):

1. Set your compass to a radius of 3 cm. To do this, open your compass so the distance between the pencil tip and the needle is 3 cm. You can measure this distance using your ruler.
2. Place the needle of your compass on point \(O\). Hold the compass steady and rotate the pencil around \(O\) to draw the full circle.

A polygon is a flat shape that is closed, has only straight sides, and has sides that do not cross each other.

Look at the shapes below. Decide if each one is a polygon.\(\quad\)\(\quad\)\(\quad\)

A triangle is a polygon with three sides.

We can classify triangles according to the number of sides that are equal in length.

An equilateral triangle is a triangle in which all three sides are equal in length and all three angles are equal.

An isosceles triangle is a triangle in which two sides are equal in length.

A scalene triangle is a triangle in which all three sides have different lengths.

A right-angled triangle is a triangle with one right angle (\(90^\circ\)).

To construct a triangle \(ABC\) with \(AB = 3\) cm, \(AC = 6\) cm, and \(BC = 5\) cm:

1. Draw the segment \(\Segment{AB}\) of length 3 cm using your ruler.
2. Draw an arc with center A and radius 6 cm using your compass.
3. Draw an arc with center \(B\) and radius 5 cm using your compass.
4. Mark the point \(C\) at the intersection of the two arcs, then draw the segments \(\Segment{AC}\) and \(\Segment{BC}\) using your ruler.

A quadrilateral is a polygon with four sides.

Some quadrilaterals are given special names, based on their side lengths, angles, and whether opposite sides are parallel.

A parallelogram is a quadrilateral in which opposite sides are parallel.

The opposite sides of a parallelogram are equal in length.

A square is a quadrilateral with four right angles and four equal sides.

A rectangle is a quadrilateral with four right angles.

The opposite sides of a rectangle are equal in length and parallel.

A rhombus is a quadrilateral with four equal sides.

The opposite sides of a rhombus are parallel.