Triangle Quiz: Interior and Exterior Angles, How Many Sides?

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Questions and Answers

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 Signup and view all the answers

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

shape, size Signup and view all the answers

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 Signup and view all the answers

What is a polygon?

A shape formed with three or more points joined by three or more straight lines. Signup and view all the answers

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. Signup and view all the answers

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. Signup and view all the answers

How are irregular polygons different from regular polygons?

Irregular polygons have sides of unequal lengths or angles with different amplitudes. Signup and view all the answers

What are non-polygons?

Non-polygons are 2D shapes that have curved sides. Signup and view all the answers

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

They are related to the sides and vertices of the polygon. Signup and view all the answers

What is an interior angle of a polygon?

Angle formed on the inside of a polygon by two adjacent sides. Signup and view all the answers

Define an exterior angle of a polygon.

Angle formed on the exterior of a polygon by extending one of the sides. Signup and view all the answers

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. Signup and view all the answers

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

Always in the same direction. Signup and view all the answers

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

180º Signup and view all the answers

What are adjacent interior angles in a polygon?

Adjacent interior angles share a side. Signup and view all the answers

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.

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Description

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.

Triangles: Interior and Exterior Angles