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Triangles

Phoenixshade

Created on August 12, 2023

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Transcript

triangles

what WE'LL learn

what is a triangle?
Types of triangles
  • Based on sides
  • Based on angles
Congruence of triangle

What is a triangle?

  • A triangle is a polygon with three edges and three vertices.
  • It is one of the basic shapes in geometry.
  • A triangle with vertices say A,B, and C is denoted ABC

Types of triangles

Based on side:
  • Scalene
  • Isosceles
  • Equilateral
Based on angles:
  • Acute-angled
  • Obtuse-angled
  • Right-angled

Scalene triangle

When a triangle has three unequal sides or angles it is called scalene triangle.

Isosceles triangle

When a triangle has two eqaul sides or equal angles then it is called isosceles triangle.

Equilateral triangle

when a triangle has three equal sides or angles it is called equilateral triangle.

Right-angled triangle

Acute angle triangle

Obtuse angle triangle

If one of the angle in the triagle is greater than 90° then it is obtuse angled triangle.

If one of the angle in the triagle is less than 90° then it is acute angled triangle.

If one of the angle in the trianhle is 90° then it is right-angled triangle.

Congruence of triangles

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. The symbol of congruence is '≅’.

Congruency Rules

  • SSS (Side-Side-Side)
  • SAS (Side-Angle-Side)
  • ASA (Angle-Side-Angle)
  • AAS (Angle-Angle-Side)
  • RHS (Right angle-Hypotenuse-Side)

Congruency Rules

SSS (Side-Side-Side)
SAS (Side-Angle-Side)

If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

If any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

Congruency Rules

ASA (Angle-Side-Angle)

If any two angles and the side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

AAS (Angle-Angle-Side)

Congruency Rules

RHS (Right angle- Hypotenuse-Side)

If the hypotenuse and a side of a right- angled triangle is equivalent to the hypotenuse and a side of the second right- angled triangle, then the two right triangles are said to be congruent by RHS rule.

THANK YOU