Relationships among angles and sides of a triangle; relationships among angles and sides of two triangles; triangle inequality theorem; rigid transformations / isometries - transla... Relationships among angles and sides of a triangle; relationships among angles and sides of two triangles; triangle inequality theorem; rigid transformations / isometries - translations, reflections, rotation.
Understand the Problem
The question covers various concepts related to triangle geometry and transformations, including the relationships between angles and sides of triangles, the properties of multiple triangles, the triangle inequality theorem, and rigid transformations such as translations, reflections, and rotations.
Answer
Angles and sides of triangles relate by angle-side relationships, the triangle inequality theorem, and rigid transformations.
The relationships among angles and sides of a triangle include: the angle-side relationship, triangle inequality theorem, and the implications of rigid transformations (translations, reflections, rotations) on triangles. These relationships help determine congruence and similarity between triangles.
Answer for screen readers
The relationships among angles and sides of a triangle include: the angle-side relationship, triangle inequality theorem, and the implications of rigid transformations (translations, reflections, rotations) on triangles. These relationships help determine congruence and similarity between triangles.
More Information
The angle-side relationship indicates that the largest angle is opposite the longest side and the smallest angle is opposite the shortest side. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Tips
A common mistake is to assume side lengths are given directly by angles; instead, use triangle inequality and trigonometric relationships to determine them.
Sources
- Trig Side and Angle Relationships - yoshiwarabooks.org
- Isometries and Coordinate Geometry - educationrealist - educationrealist.wordpress.com
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