PPT: A Tale of Three Intersecting Lines | Mathematics Olympiad Class 7 PDF Download

 Page 1


A Tale of Three 
Intersecting Lines
Page 2


A Tale of Three 
Intersecting Lines
Introduction
Triangles Everywhere
From cheese slices to 
towering bridges, triangles 
are all around us. They're 
simple yet profound building 
blocks for complex 
structures.
Three Key Components
Vertices: Three corner points 
where lines meet. Sides: 
Three straight line segments 
forming the boundary. 
Angles: Three internal 
angles.
Fundamental Shape
A triangle is the most basic 
closed shape you can make 
with straight lines, yet holds 
surprising depth.
Page 3


A Tale of Three 
Intersecting Lines
Introduction
Triangles Everywhere
From cheese slices to 
towering bridges, triangles 
are all around us. They're 
simple yet profound building 
blocks for complex 
structures.
Three Key Components
Vertices: Three corner points 
where lines meet. Sides: 
Three straight line segments 
forming the boundary. 
Angles: Three internal 
angles.
Fundamental Shape
A triangle is the most basic 
closed shape you can make 
with straight lines, yet holds 
surprising depth.
Understanding Triangles
Vertices
The corner points where 
sides intersect. Think of 
them as the 'tips' of the 
triangle.
Sides
The straight line segments 
connecting each pair of 
vertices, forming the 
triangle's boundary.
Naming Triangles
We name triangles using 
their vertices. For example, if 
vertices are labeled A, B, and 
C, we call it &ABC.
Page 4


A Tale of Three 
Intersecting Lines
Introduction
Triangles Everywhere
From cheese slices to 
towering bridges, triangles 
are all around us. They're 
simple yet profound building 
blocks for complex 
structures.
Three Key Components
Vertices: Three corner points 
where lines meet. Sides: 
Three straight line segments 
forming the boundary. 
Angles: Three internal 
angles.
Fundamental Shape
A triangle is the most basic 
closed shape you can make 
with straight lines, yet holds 
surprising depth.
Understanding Triangles
Vertices
The corner points where 
sides intersect. Think of 
them as the 'tips' of the 
triangle.
Sides
The straight line segments 
connecting each pair of 
vertices, forming the 
triangle's boundary.
Naming Triangles
We name triangles using 
their vertices. For example, if 
vertices are labeled A, B, and 
C, we call it &ABC.
Angles of a Triangle
Three Internal 
Angles
For &ABC, the 
angles are 
"CAB (at vertex 
A), "ABC (at 
vertex B), and 
"BCA (at vertex 
C).
Simplified 
Notation
Often, we 
simplify and just 
call them "A, 
"B, and "C.
Collinear Points
If three points lie on a single straight line, 
they cannot form a triangle - just a line 
segment.
Page 5


A Tale of Three 
Intersecting Lines
Introduction
Triangles Everywhere
From cheese slices to 
towering bridges, triangles 
are all around us. They're 
simple yet profound building 
blocks for complex 
structures.
Three Key Components
Vertices: Three corner points 
where lines meet. Sides: 
Three straight line segments 
forming the boundary. 
Angles: Three internal 
angles.
Fundamental Shape
A triangle is the most basic 
closed shape you can make 
with straight lines, yet holds 
surprising depth.
Understanding Triangles
Vertices
The corner points where 
sides intersect. Think of 
them as the 'tips' of the 
triangle.
Sides
The straight line segments 
connecting each pair of 
vertices, forming the 
triangle's boundary.
Naming Triangles
We name triangles using 
their vertices. For example, if 
vertices are labeled A, B, and 
C, we call it &ABC.
Angles of a Triangle
Three Internal 
Angles
For &ABC, the 
angles are 
"CAB (at vertex 
A), "ABC (at 
vertex B), and 
"BCA (at vertex 
C).
Simplified 
Notation
Often, we 
simplify and just 
call them "A, 
"B, and "C.
Collinear Points
If three points lie on a single straight line, 
they cannot form a triangle - just a line 
segment.
Equilateral Triangles
Equal Sides
All three sides 
have the same 
length.
Perfect 
Symmetry
Equilateral 
triangles stand 
out for their 
perfect symmetry.
Equal Angles
All angles are 
equal, each 
measuring 60 
degrees.