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Chapter 8: Problem 8

State the characteristics of each triangle. Scalene triangle

Short Answer

Expert verified
A scalene triangle has no congruent sides or angles, and no lines of symmetry.

Step by step solution

01

Define a Scalene Triangle

A scalene triangle is a triangle with all three sides of different lengths. Consequently, all three angles are also of different measures.
02

Analyze Side Lengths

In a scalene triangle, since all sides have different lengths, no two sides are congruent.
03

Analyze Angles

Because all sides have different lengths, the internal angles are also different. An internal angle opposite to a longer side is larger than an internal angle opposite to a shorter side.
04

Symmetry

A scalene triangle does not have any lines of symmetry because the sides and angles are all different.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

triangle types
Triangles are one of the fundamental shapes in geometry. They come in various types based on side lengths and angle measurements. There are mainly three types of triangles by sides:
  • Scalene Triangle: All three sides and angles are different.
  • Isosceles Triangle: Two sides (and their opposite angles) are equal.
  • Equilateral Triangle: All three sides (and angles) are equal.
Understanding these basic types helps in solving various geometry problems and recognizing different triangle properties.
triangle properties
Each type of triangle has unique properties. Here鈥檚 a closer look:
  • Scalene Triangle Properties: No equal sides, all angles different, no lines of symmetry.
  • Isosceles Triangle Properties: Two equal sides, two equal angles, one line of symmetry.
  • Equilateral Triangle Properties: Three equal sides, all angles are 60 degrees, three lines of symmetry.
For scalene triangles, it's important to note the relationship between side lengths and angles. The angle opposite the longest side is the largest. This understanding assists in identifying unknown angles or sides.
geometry basics
Fundamentals of geometry include understanding different shapes, their properties, and relationships. Triangles are a crucial part of this. Some key points to remember are:
  • Angles in a Triangle: The sum of all internal angles in any triangle is always 180 degrees.
  • Congruency and Similarity: Triangles can be congruent (same shape and size) or similar (same shape, different sizes).
  • Triangle Inequality Theorem: The sum of any two sides of a triangle must be greater than the third side.
Mastering these basics helps in understanding more complex properties and solving advanced geometry problems efficiently.

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