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TRIANGLES in One Shot - From Zero to Hero || Class 9th

Physics Wallah Foundation・2 minutes read

The chapter on Triangles in the Class Ninth Revision Video Series explores different types of triangles based on sides and angles, delving into properties such as angle sum and congruence criteria. It provides a comprehensive understanding of triangles and their unique aspects, aiming to help students grasp key concepts effectively.

Insights

  • Triangles have unique properties such as interior angles adding up to 180 degrees and different classifications based on side lengths and angles, including equilateral, isosceles, and scalene triangles.
  • The congruence of triangles can be determined by comparing corresponding sides and angles, with rules like Side-Angle-Side (SAS) and Angle-Side-Angle (ASA) providing criteria for establishing congruence, leading to a deeper understanding of geometric relationships and proofs.

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Recent questions

  • What are the different types of triangles?

    Equilateral, isosceles, scalene based on side lengths.

  • How is the perimeter of a triangle defined?

    Sum of lengths of its three sides.

  • What are the classifications of triangles based on angles?

    Right angle, acute angle, obtuse angle triangles.

  • How are exterior angles formed in a triangle?

    When one side is extended.

  • What is the sum of interior angles in a triangle?

    Proven to be 180 degrees.

Related videos

Summary

00:00

Exploring Triangles: Geometry Essentials in Class Nine

  • The chapter being discussed is Triangles in the Class Ninth Revision Video Series.
  • The entry into geometry occurred after reading Chapter Five Euclid Geometry, followed by Lines and Angles, and now focusing on Triangles.
  • The chapter delves into the unique aspects of triangles, such as interior angles measuring 80 degrees.
  • Different types of triangles are explored, including equilateral triangles where all sides are equal, isosceles triangles with two equal sides, and scalene triangles with all sides of different lengths.
  • The perimeter of a triangle is defined as the sum of the lengths of its three sides.
  • Triangles are classified based on angles as right angle triangles (with one 90-degree angle), acute angle triangles (all angles less than 90 degrees), and obtuse angle triangles (one angle greater than 90 degrees but less than 180 degrees).
  • The sum of interior angles in a triangle is proven to be 180 degrees, with exterior angles formed when one side of a triangle is extended.
  • A question is presented where the angles of a triangle are in a 4:6 ratio, leading to the calculation of each angle.
  • Another question involves proving that the angle BOC is equal to 90 degrees plus half of angle A when the bisectors of angles B and C intersect at point O.
  • The chapter aims to provide a comprehensive understanding of triangles, their properties, and various types based on sides and angles.

13:44

Triangle Properties and Bisex Relationship Explained

  • Bisex is a concept that may have encountered issues.
  • When writing X along with Bisex, consider the relationship between parts.
  • In a triangle ABC, explore the properties of angle sum.
  • The sum of angles A, B, and C in a triangle is 180°.
  • Understand the calculations for angles A and B in a triangle.
  • Learn how to properly cut a pumpkin to understand division.
  • Applying angle sum property in triangles helps determine angle relationships.
  • Congress Figures refer to geometric figures with congruent sides and angles.
  • To determine if two triangles are congruent, compare their corresponding sides and angles.
  • The criteria for congruence in triangles involve equal sides and angles between them.

28:51

Proving Triangle Congruence with SAS and ASA

  • The postulate should have been in Euclid's book but isn't explicitly written.
  • If the corresponding sides and included angles of two triangles are equal, they are congruent.
  • The process of constructing triangles involves matching sides and angles.
  • The proof of the theorem involves understanding the given angles and sides of the triangles.
  • By using the Side-Angle-Side (SAS) rule, the congruence of triangles can be proven.
  • If one side of a triangle is larger, it can be adjusted by constructing a point on the side.
  • The angles of the triangles will be equal if the remaining angle becomes zero degrees.
  • Collinear points indicate that two triangles are concurrent.
  • The Angle-Side-Angle (ASA) criteria can be used to prove the congruence of triangles.
  • Corollaries are extensions of theorems, providing additional results based on the original theorem.

46:56

Triangle Congruence and Angle Bisectors

  • Draw the bisector of angle A and intersect it with point D to form angle B.
  • Identify the bisector of angle B and intersect it with point E.
  • Determine the intersection point of the bisector of angle B with line DE.
  • Analyze the resulting triangles CR and BA.
  • Establish the equality of angles in triangles CR and BA.
  • Confirm the equality of angles C and A in triangles CR and BA.
  • Apply the side-angle-side criteria to triangles CR and BA.
  • Utilize the CPCT (Corresponding Parts of Congruent Triangles) principle.
  • Discuss the side-side-side congruence criteria for triangles ABC and PQR.
  • Explain the concept of right-angled triangles and the RHS (Right Angle-Hypotenuse-Side) rule for congruence.

01:08:07

Equal Lengths and Angles in Triangle ABC

  • Length of B and C will be equal in triangle ABC.
  • Angle A is equal to 90° in triangles ADB and ACI.
  • By congruency of triangles ADB and ACI, it is proven that B = C.
  • In triangle ABC, the lengths from D to C are equal, proven by CPCT.
  • CD bisects AB, proving that OA = OB by AAS corollary and CPCT.
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