#### Need Help?

Get in touch with us

## Key Concepts

• Find the shortest distance between a point and a line.
• Find the shortest distance between two parallel lines.
• Define the perpendicular transversal theorem.
• Define the lines perpendicular to a transversal theorem.
• Theorem: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
• Theorem: If two lines are perpendicular, then they intersect to form four right angles.
• Theorem: If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

#### 1. Shortest distance from a point to a line

The distance from a point to a line is the length of the perpendicular segment from the point to the line. This perpendicular segment is the shortest distance between the point and the line.

#### 2. Shortest distance between two parallel lines

The distance between two parallel lines is the length of any perpendicular segment joining the two lines.

#### 3. Perpendicular transversal theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

#### 4. Lines perpendicular to a transversal theorem

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

#### 5. Theorem

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

#### 6. Theorem

If two lines are perpendicular, then they intersect to form four right angles.

#### 7. Theorem

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

## Exercise

1. Find m∠1.
1. In the diagram, , (FG) ⊥ (GH) Find the value of
1. Determine which lines, if any, must be parallel. Explain your reasoning.
1. Find all the unknown angle measures in the diagram at the right. Justify your reasoning for each angle measure.
1. Find all the unknown angle measures in the diagram at the right. Justify your reasoning for each angle measure.

## What we have learned

• The distance from a point to a line is the length of the perpendicular segment from the point to the line.
• The distance between two parallel lines is the length of any perpendicular segment joining the two lines.
• Theorem: If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
• Theorem: If two lines are perpendicular, then they intersect to form four right angles.
• Theorem: If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.

#### Composite Figures – Area and Volume

A composite figure is made up of simple geometric shapes. It is a 2-dimensional figure of basic two-dimensional shapes such as squares, triangles, rectangles, circles, etc. There are various shapes whose areas are different from one another. Everything has an area they occupy, from the laptop to your book. To understand the dynamics of composite […] #### Special Right Triangles: Types, Formulas, with Solved Examples.

Learn all about special right triangles- their types, formulas, and examples explained in detail for a better understanding. What are the shortcut ratios for the side lengths of special right triangles 30 60 90 and 45 45 90? How are these ratios related to the Pythagorean theorem?  Right Angle Triangles A triangle with a ninety-degree […] #### Ways to Simplify Algebraic Expressions

Simplify algebraic expressions in Mathematics is a collection of various numeric expressions that multiple philosophers and historians have brought down. Talking of algebra, this branch of mathematics deals with the oldest concepts of mathematical sciences, geometry, and number theory. It is one of the earliest branches in the history of mathematics. The study of mathematical […]   