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This lesson will provide information and guidance on:
- Complementary Angles,
- Supplementary Angles,
- Opposite Angles,
- Corresponding and Alternate Angles, and
- Sum of Interior Angles in Triangles and in Quadrilaterals.
After reviewing the lessons above you will be ready to read through the information below on angles and their relationships with your children. Discuss these as you go and, when you are ready, try the angle relationships worksheet.
Parallel Lines - lines that are equidistant from each other and never intersect.
Transversal - a line that intersects two or more other lines.
Adjacent Angles - angles that share a common side and that have a common vertex.
Complementary Angles are those which add together to make 90°.
|∠ABD + ∠DBC = 90°|
|These two angles are complementary because they add together to make 90°.60° + 30° = 90°|
|These two angles are also complementary.15° + 75 ° = 90°|
The examples above all show two angles that are complementary. Notice that the angles do not have to be adjacent to be complementary. If they are adjacent then they form a right angle.
Supplementary Angles add together to make 180°
|125° + 55° = 180°|
The two angles shown above are supplementary to each other. They add together to give 180°. They can be said supplement each other. Note that, as with complementary angles, they do not need to be adjacent to each other.
When to lines intersect they create four angles. Each angle is opposite to another and form a pair of what are called opposite angles.
|Angles a and c are opposite angles.
Angles b and d are opposite angles
|Opposite angles are equal.
The two 130° angles are opposite as
are the two 50° angles.
Opposite angles are sometimes called vertical angles or vertically opposite angles.
Corresponding and Alternate Angles
The example below shows two parallel lines and a transversal (a line that cross two or more other lines). This results in eight angles. Each of these angles has a corresponding angle. Looking at the two intersections, the angles that are in the same relative (or corresponding) positions are called corresponding angles.
Since the two lines are parallel, the corresponding angles are equal.
|a and e are corresponding angles
b and f are corresponding angles
c and g are corresponding angles
d and h are corresponding angles
As Shown below, there are also two pairs of alternate interior angles and two pairs of alternate exterior angles. Notice how the interior angles are in between the two parallel lines and the exterior angles are to the outside.
|a and g are alternate exterior angles
b and h are alternate exterior angles
c and e are alternate interior angles
d and f are alternate interior angles
Since the two lines are parallel, the alternate angles shown above are equal.
The Sum of Interior Angles
The sum of the interior angles in a triangle is 180°.
The sum of the interior angles in a quadrilateral is 360°.
Try the 180° In a Triangle Experiment which is a 2-page (be careful with the scissors) activity to demonstrate that the sum of the interior angles in a triangle is 180°.
Angle Relationship Worksheet
Have your children try the worksheet below that has questions on angle relationships. After completing it your children will be ready to review the lesson on finding missing angles.