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Questions and Answers
What type of triangle has all sides equal?
In a right triangle, what is the measure of one angle?
Which triangle type has at least one angle larger than 90 degrees?
What is the characteristic of an isosceles triangle?
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If a triangle has sides measuring 12 cm, 15 cm, and 20 cm, what type of triangle is it?
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Study Notes
Exploring Triangle Types
The study of triangles encompasses various categories based on the sides' and angles' characteristics. Understanding these distinctions enhances our ability to recognize and analyze distinct triangle shapes effectively.
Side Length Based Classification
| Type | Description | Example(s) |
|---|---|---|
| Equilateral | All sides are equal | ΔABC, with AB = AC = BC |
| Isosceles | At least two sides are equal | ΔPQR, with PQ = PR |
| Scalene | None of the sides are equal | ΔXYZ, with XY ≠ YZ ≠ ZX |
Angle Size Based Classification
| Type | Characteristic | Example(s) |
|---|---|---|
| Acute | All angles are acute | Any triangle whose angles meet this condition |
| Right | One angle equals ( 90^\circ) | ΔDEF, with DFE = (90^\circ) |
| Obtuse | At least one angle exceeds ( 90^\circ) | ΔGHI, with HIG > (90^\circ) |
These guidelines help us understand how triangles may be categorized. For instance, consider a triangle like the Flight Path shown in Figure 1:
With lengths of 20 cm, 20 cm, and 31 cm, and angles measured at 40°,\ (40^\circ), and 100°, it would fall under the category of Scalene Isosceles Obtuse Triangle due to having two equal sides and one angle larger than 90°.
As mathematically curious explorers, mastering the basics of triangle classifications provides a solid foundation upon which we can build deeper insights into geometry's intricate patterns and relationships.
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Description
Enhance your understanding of different triangle types based on side lengths and angle sizes. Learn to classify triangles as Equilateral, Isosceles, Scalene, Acute, Right, or Obtuse based on unique characteristics. Practice identifying triangle shapes using examples and visual aids.
