key term - Supplementary Angles

Definition

Supplementary angles are a pair of angles that add up to 180 degrees. They are angles that are opposite each other and form a straight line. This concept is important in understanding the properties of angles, triangles, and other geometric shapes.

5 Must Know Facts For Your Next Test

1. Supplementary angles are always on opposite sides of the intersection point when two lines cross.
2. If two angles are supplementary, then the sum of their measures is always 180 degrees.
3. Supplementary angles can be used to find missing angle measures in triangles and other polygons.
4. Supplementary angles are important in the Pythagorean Theorem, which relates the sides of a right triangle.
5. Supplementary angles are also relevant in the properties of rectangles, where opposite angles are supplementary.

Review Questions

• Explain how supplementary angles can be used to find missing angle measures in a triangle.
  • In a triangle, the sum of the three angles is always 180 degrees. If you know the measure of two angles in a triangle, you can use the fact that the third angle is supplementary to the other two. For example, if one angle is 60 degrees and another is 80 degrees, the third angle must be 180 - 60 - 80 = 40 degrees, since the three angles are supplementary.
• Describe how supplementary angles are related to the Pythagorean Theorem.
  • The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This relationship is dependent on the fact that the two acute angles in a right triangle are supplementary, meaning they add up to 90 degrees. The Pythagorean Theorem would not hold true if the angles were not supplementary.
• Analyze how supplementary angles are used in the properties of rectangles.
  • In a rectangle, the opposite angles are always supplementary, meaning they add up to 180 degrees. This is because a rectangle is a quadrilateral with four right angles. Since the angles at each vertex of a rectangle are 90 degrees, the opposite angles must be supplementary in order for the sum of the angles to be 360 degrees, as required for a closed polygon. Understanding the relationship of supplementary angles in rectangles is crucial for applying properties like the diagonals bisecting each other and being congruent.

Related terms

Complementary Angles:

Complementary angles are a pair of angles that add up to 90 degrees. They are angles that are adjacent to each other and form a right angle.

Vertical Angles:

Vertical angles are a pair of opposite angles formed when two lines intersect. Vertical angles are always congruent, meaning they are equal in measure.

Parallel Lines:

Parallel lines are lines that never intersect and are always the same distance apart. The angles formed when parallel lines are cut by a transversal line have special relationships, including supplementary angles.