Triangle Types and Basic Properties

This page introduces fundamental triangle concepts and classifications. The content covers various triangle types and their unique characteristics, with special attention to angle and side relationships.

Definition: A triangle is a three-sided polygon where the sum of all internal angles equals 180 degrees.

Vocabulary:

• Hypotenuse: The longest side of a right triangle, opposite to the right angle
• Katheten: The two shorter sides of a right triangle

Highlight: In a right triangle, one angle must be exactly 90 degrees, while in an equilateral triangle, all sides and angles are equal (60 degrees each).

Example: The isosceles triangle (gleichschenkliges Dreieck) has two equal sides and two equal angles, making it symmetrical along its height.

Triangle Construction Methods

This page details various triangle construction methods using specific measurements of sides and angles. The content focuses on four main construction approaches: SSS (three sides), SSW (two sides and one angle), SWS (two sides and the included angle), and WSW (two angles and the included side).

Definition: SSS (Side-Side-Side) construction requires three known side lengths to create a unique triangle.

Highlight: When constructing triangles, always start with the longest side as the base for more accurate results.

Example: For SSS construction:

1. Draw the first side
2. Use compass to create arcs from both endpoints
3. The intersection point forms the third vertex

Advanced Triangle Construction

This page focuses on the WSW (Angle-Side-Angle) construction method, which is one of the most reliable ways to construct a triangle when two angles and the included side are known.

Definition: WSW construction requires two angles and the side between them to create a unique triangle.

Highlight: The WSW method is particularly useful because knowing two angles automatically determines the third angle (180° - sum of known angles).

Example: To construct a triangle using WSW:

1. Draw the given side (6cm)
2. Construct the given angles (40° and 60°) from each endpoint
3. Extend the angle lines until they intersect to form the triangle