Classifying Triangles and Their Properties

What is the sum of the interior angles in any triangle?

If angle DCA measures 138°, what is the measure of angle BCA if the angles on a line add up to 180°?

How does the measure of an exterior angle relate to the two non-adjacent interior angles in a triangle?

Can a right-angled triangle also be classified as an obtuse triangle?

What is a general rule for the relationship between the angles inside a triangle and the angles inside a rectangle?

Which type of triangle has all angles less than $90^{ ext{o}}$?

What is a defining characteristic of an obtuse triangle?

How many vertices does a triangle have?

What can be said about a right-angled triangle?

If a triangle has angles measuring $30^{ ext{o}}$, $60^{ ext{o}}$, and $90^{ ext{o}}$, which type is it?

What happens to the angles in any triangle regarding their sum?

Which statement about triangle classifications is true?

What is the minimum number of angles that need to be known to classify a triangle?

Museum of Modern Art

The Museum of Modern Art in Bonn, Germany features three tall, blue cone-shaped structures with glass roofs.
The structures are situated in a garden setting, with landscaping and a flat roof.

Triangles

Triangles are shapes with three angles and three sides.
They can be classified by their side lengths and angle measurements.

Classifying Triangles

Acute Triangles: All angles are less than 90 degrees.
Obtuse Triangles: One angle is greater than 90 degrees.
Right-Angled Triangles: One angle is exactly 90 degrees.
A triangle cannot be classified as both obtuse and acute simultaneously, as these classifications describe distinct angle relationships.

Interior Angles of a Triangle

The sum of the interior angles of any triangle always equals 180 degrees.

ATL1

When folding the angles of a triangle inward so the vertices touch, the resulting shape demonstrates that the angles of a triangle sum to 180 degrees.
Ripping off the corners of a triangle and placing them adjacent to each other allows for the visual representation of the angles adding up to 180 degrees.

Reflect and Discuss 9

A right-angled triangle cannot also be an obtuse triangle because an obtuse triangle requires one angle greater than 90 degrees, while a right-angled triangle already has a 90-degree angle.
The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles (A + B).
The sum of the angles inside a triangle (180 degrees) is half the sum of the angles inside a rectangle (360 degrees) since a rectangle can be divided into two congruent triangles.

Example 3

Angles on a straight line add up to 180 degrees.
The sum of the interior angles of a triangle is 180 degrees.
Knowing two angles in a triangle allows you to calculate the third angle using the fact that the angles sum to 180 degrees.

This quiz explores the classification of triangles based on their angles and sides, including acute, obtuse, and right-angled triangles. Additionally, it discusses the fundamental property that the sum of the interior angles of a triangle always equals 180 degrees.