Triangles: Interior and Exterior Angles

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18 Questions

A triangle is a polygon with ______ angles and ______ sides.

three, three

The sum of the interior angles of a triangle is always equal to ______.

180º

The sum of the exterior angles of a triangle is always equal to ______.

360º

The exterior angles of a triangle are equal to the sum of the two opposite ______ angles.

interior

Two triangles are congruent (equal) when they have the same ______ and ______.

shape, size

The angle with the biggest amplitude is opposite to the side with the biggest ______. The angle with the smallest amplitude is opposite to the side with the smallest ______.

length, length

What is a polygon?

A shape formed with three or more points joined by three or more straight lines.

How is the name of a polygon related to its characteristics?

The name of the polygon is related to the number of sides that it has.

What are the conditions for a polygon to be classified as regular?

All the sides have equal lengths and all the interior angles have the same amplitude.

How are irregular polygons different from regular polygons?

Irregular polygons have sides of unequal lengths or angles with different amplitudes.

What are non-polygons?

Non-polygons are 2D shapes that have curved sides.

What are the interior and exterior angles of a polygon related to?

They are related to the sides and vertices of the polygon.

What is an interior angle of a polygon?

Angle formed on the inside of a polygon by two adjacent sides.

Define an exterior angle of a polygon.

Angle formed on the exterior of a polygon by extending one of the sides.

What is the relationship between the interior and exterior angles that are adjacent in a polygon?

They add up to 180º, so they are supplementary.

What do the exterior angles of a polygon add up to?

Always in the same direction.

What is the sum of an interior angle and its corresponding exterior angle in a polygon?

180º

What are adjacent interior angles in a polygon?

Adjacent interior angles share a side.

Study Notes

Polygon Characteristics

  • A triangle is a polygon with three angles and three sides.

Angle Properties

  • The sum of the interior angles of a triangle is always equal to 180 degrees.
  • The sum of the exterior angles of a triangle is always equal to 360 degrees.
  • The exterior angles of a triangle are equal to the sum of the two opposite interior angles.

Congruent Triangles

  • Two triangles are congruent (equal) when they have the same shape and size.

Angle-Side Relationships

  • The angle with the biggest amplitude is opposite to the side with the biggest length.
  • The angle with the smallest amplitude is opposite to the side with the smallest length.

Polygon Definitions

  • A polygon is a 2D shape with at least three sides.
  • The name of a polygon is related to its characteristics, with the Greek prefix indicating the number of sides (e.g., triangle for three sides, quadrilateral for four sides).

Regular and Irregular Polygons

  • A polygon is classified as regular if all its sides and angles are equal.
  • Irregular polygons are different from regular polygons because they do not have equal sides and angles.

Non-Polygons

  • Non-polygons are shapes that do not have at least three sides.

Angle Relationships

  • The interior and exterior angles of a polygon are related in that they add up to 180 degrees when adjacent.
  • An interior angle of a polygon is an angle inside the polygon.
  • An exterior angle of a polygon is an angle outside the polygon, formed by extending a side.
  • The sum of an interior angle and its corresponding exterior angle in a polygon is 180 degrees.
  • Adjacent interior angles in a polygon are angles that share a side.

This quiz covers the interior and exterior angles of triangles, types of triangles based on angles and sides, and the relationship between angles and sides. It also explores concepts such as triangular congruence and the triangular inequality, as well as the sum of interior and exterior angles in triangles.

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