Geometry Review
Triangles
A triangle is a polygon with three edges and three vertices. All triangles have internal angles that equal 180
degrees.
There are six types of triangles which can be classified by either their side lengths or angle measurements.
Triangles classified by their side measurement are equilateral, isosceles, and scalene.
Triangles classified by their angle measurements are right, acute, and obtuse
Quadrilaterals
A quadrilateral is any two-dimensional (2-D) figure or polygon that has four straight sides. Quadrilaterals can
be classified or sorted by their different properties or characteristics.
Kites, trapezoids, parallelograms, rectangles, rhombus, and squares are different types of quadrilaterals.
This tree diagram shows the relationships between the different types of quadrilaterals.
These diagrams show that a square is a rectangle, a rhombus, a parallelogram, and a quadrilateral
Symmetry
You can find lines of symmetry on regular and irregular polygons.
Measuring Angles
Angles are classified into different types based on their measures.
Acute Angle
An angle that measures less
than 90 degrees.
Right Angle
An angle that measures
exactly 90 degrees.
Obtuse Angle
An angle that measures more
than 90 degrees but less than
180 degrees.
Straight Angle
An angle that measures
exactly 180 degrees. It forms
a straight line.
Step 1
Place the midpoint of the protractor on the vertex of the angle. The 0 degree line on the ride side of the
protractor’s inner scale should line up with the end of the bottom of the ray.
Step 2
Start at the right side of the protractor’s inner scale, at the 0 degree line, and count by tens until you
reach the number of degrees closest to the upper ray without passing it.
Step 3
Count the individual ticks after the nearest ten by ones until you reach the upper ray of the angle.
Drawing Angles
Draw an angle that is 145 degrees.
Step 1
Draw a ray.
Step 2
Place the protractor on the ray so that the midpoint of the protractor lines up with the end of the ray.
Step 3
Starting at 0 degrees, count the number of degrees needed to construct the angle.
If the ray is pointing to the right, always use the inside of the scale. If the ray is pointing to the left, use
the outside scale. Always start measuring at 0 degrees.
The angle needs to 145 degrees, so stop at 145. Using your pencil, mark the point that shows 145
degrees.
Step 4
Remove the protractor, and join the point that you marked and the endpoint of the ray that was drawn.
Drawing Polygons
To construct an isosceles triangle with a base measuring 4cm and two congruent angles of 45 degrees, use the
following steps.
Step 1
Using a ruler, draw a line segment that is 4cm long.
Step 2
At one endpoint of the line segment, construct a 45 degree angle using a protractor. At the other
endpoint of the line segment, construct another 45 degree angle using a protractor.
Step 3
The two rays of the constructed angles will intersect to form the third angle of the triangle. Since the
total number of degrees in any triangle is 180 degrees, the measure of the third angle is 90 degrees.
Your completed isosceles triangle should look like the triangle below