Triangle and Its Types mathematics .pptx

triangles,types of triangles

1. Triangle and Its Types Add description Name

2. Basics of Triangle 01 Equilateral Triangle 02 Isosceles Triangle 03 Scalene Triangle 04 Right Triangle 05 Obtuse Triangle 06 Contents

3. Basics of Triangle 01

4. Definition of Triangle A triangle is a closed plane figure formed by three line segments. Closed Plane Figure Three intersecting lines that create three angles and three sides. Three Intersecting Lines A triangle has three vertices and three straight sides connecting them. Three Vertices and Sides

5. Properties of Triangle 01 Triangles have three internal angles that sum to 180 degrees. Fundamental Angles 02 The length of a triangle's sides determines the size of its angles. Side-Angle Relationship 03 Triangles with matching sides and angles are considered congruent. Congruent Triangles

6. Types of Triangles Sides and angles are equal. Equilateral Triangle Two equal sides and angles. Isosceles Triangle 02 01 All sides and angles are unequal. Scalene Triangle 03

7. Equilateral Triangle 02

8. Characteristics All three sides are of equal length. Equal Sides All three angles are 60 degrees. Equal Angles The triangle is perfectly symmetrical. Symmetrical

9. Congruence and Similarity Equilateral triangles have all sides and angles congruent, resulting in similar triangles. Equal Sides and Angles Equilateral triangles exhibit perfect symmetry and regularity, making them visually appealing. Symmetry and Regularity

10. Congruence and Similarity Equilateral triangles possess unique properties, such as all angles being 60 degrees. Unique Properties

11. Applications Structural Stability Equilateral triangles provide high structural integrity for buildings and bridges. Decorative Patterns Equilateral triangles are commonly used in decorative designs and artwork. Efficient Tessellation Equilateral triangles efficiently tessellate a surface with minimal gaps.

12. Isosceles Triangle 03

13. Characteristics Two sides of the isosceles triangle are equal in length. Equal Sides The two angles opposite the equal sides are also equal. Equal Angles The perpendicular bisector of the base is also the axis of symmetry. Perpendicular Bisector

14. Congruence and Similarity Isosceles triangles have two congruent sides. Congruent Sides Isosceles triangles have two congruent angles. Congruent Angles Isosceles triangles are similar to each other. Similar Triangles

15. Applications Isosceles triangles provide enhanced structural stability in architecture and engineering. Structural Stability 01 Roof Design 02 Isosceles triangles are commonly used in roof design for their aesthetic appeal and load-bearing capabilities.

16. Applications Isosceles triangles offer mechanical advantage in simple machines like pulleys and levers. Mechanical Advantage

17. Scalene Triangle 04

18. Characteristics All three sides of a scalene triangle are of different lengths. Unequal Sides The three angles of a scalene triangle are also unequal. Unequal Angles A scalene triangle does not have any congruent sides. No Congruent Sides

19. Congruence and Similarity Unique Side Lengths Scalene triangles have three unique side lengths, leading to distinct congruence and similarity properties. Angle Measures The three angles in a scalene triangle are all different, affecting congruence and similarity.

20. Congruence and Similarity Scalene triangles exhibit unique characteristics that differentiate them from other triangle types. Unique Characteristics

21. Applications Scalene triangles provide enhanced structural stability in engineering designs. Structural Stability Scalene triangles are commonly used in roof framing for their strength. Roof Framing Scalene triangles form the basis of suspension bridge design. Suspension Bridges

22. Right Triangle 05

23. Characteristics 01 Two sides meet at a 90-degree angle. Perpendicular Sides 02 Longest side, opposite the right angle. Hypotenuse 03 Relationship between side lengths. Pythagorean Theorem

24. Congruence and Similarity Triangles with equal sides and angles Congruent Triangles Triangles with proportional sides and equal angles Similar Triangles

25. Applications Solving for unknown sides and angles in right triangles. Trigonometry Building stable structures like bridges and roofs. Construction Determining direction and distance using compass and maps. Navigation

26. Obtuse Triangle 06

27. Characteristics Angles Greater Than 90° An obtuse triangle has one angle greater than 90 degrees. Longest Side Opposite Obtuse Angle The longest side of an obtuse triangle is opposite the obtuse angle. Acute Angles Less Than 90° The other two angles in an obtuse triangle are acute, less than 90 degrees.

28. Congruence and Similarity Identical in all sides and angles. Congruent Obtuse Triangles Proportional in all sides and angles. Similar Obtuse Triangles 02 01 Corresponding angles are equal, sides are proportional. Angle-Side-Angle Similarity 03

29. Applications Obtuse triangles provide enhanced structural stability in architectural designs. Structural Stability Obtuse triangles effectively distribute loads in construction projects. Load Distribution Obtuse triangles are commonly used in unique roof designs. Roof Designs

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