Triangle and Polygon Properties

The video tutorial covers the applications of special right triangles, focusing on 45-45-90 and 30-60-90 triangles. It introduces key vocabulary such as altitude and diagonal, explaining their properties in different types of triangles and polygons. The tutorial includes problem-solving examples to apply these concepts, emphasizing the importance of labeling diagrams and using known ratios to find unknown values.

What are the two types of special right triangles discussed in the video?

• 60-60-60 and 45-45-90

• 30-60-90 and 60-60-60

• 30-60-90 and 45-45-90

• 30-30-60 and 60-60-60

What is the definition of the altitude of a triangle?

• A line segment from a vertex to the midpoint of the opposite side

• A line segment from a vertex perpendicular to the base

• A line segment from the midpoint of one side to the midpoint of another

• A line segment that bisects an angle

How many altitudes can be drawn in a triangle?

• Three

• Four

• Two

• One

In an isosceles triangle, what does the altitude do to the vertex angle?

• It doubles the vertex angle

• It bisects the vertex angle

• It has no effect on the vertex angle

• It trisects the vertex angle

What is a diagonal in a polygon?

• A line segment that is parallel to one side

• A line segment that bisects the polygon

• A line segment from one vertex to a non-consecutive vertex

• A line segment from one vertex to the next consecutive vertex

What is the first step in solving problems with special right triangles?

• Draw or label the diagram with known information

• Identify the type of triangle

• Find the perimeter of the triangle

• Calculate the area of the triangle

In the example problem, what is the side length of the equilateral triangle?

• 4√2

• 4

• 2√2

• 2

What is the length of the altitude in the equilateral triangle example?

• √6

• √3

• 2√6

• 2√3

In the square example, what is the length of one side if the perimeter is 24?

• 8

• 4

• 5

• 6

What is the length of the diagonal in the square example?

• 6√2

• 9√2

• 12√2

• 15√2