Definitions [7]
A triangle (denoted by the symbol △) is the simplest closed shape in geometry. It is a two-dimensional figure made by connecting three points that do not lie on the same straight line (non-collinear).
Define a triangle.
A plane figure bounded by three lines in a plane is called a triangle. The figure below represents a ΔABC, with AB, AC andBC as the three line segments.
An exterior angle is formed when a side of a triangle is extended beyond its vertex. The angle created between the extended side and the adjacent side of the triangle is the exterior angle.
The line segment joining a vertex of a triangle to the midpoint of its opposite side is called a median of the triangle.
- The point where all three medians meet is called the centroid.
In similar triangles, the angles opposite to proportional sides are the corresponding angles, and so, they are equal.
-
∠A = ∠P
-
∠B = ∠Q
-
∠C = ∠R
In similar triangles, the sides opposite to equal angles are said to be the
corresponding sides.
ΔABC ∼ ΔPQR
\[\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}\]
Two triangles are similar if
- Their corresponding angles are equal, and
- Their corresponding sides are proportional.
- Symbolically:
ΔABC ∼ ΔPQR (read as “ABC is similar to PQR”).
Concepts [15]
- Basic Concepts of Triangles
- Remote Interior Angles of a Triangle Theorem
- Exterior Angle of a Triangle and Its Property
- Congruence of Triangles
- Isosceles Triangles Theorem
- Converse of Isosceles Triangle Theorem
- Corollary of a Triangle
- Property of 30°- 60°- 90° Triangle Theorem
- Property of 45°- 45°- 90° Triangle Theorem
- Median of a Triangle
- Property of Median Drawn on the Hypotenuse of Right Triangle
- Perpendicular Bisector Theorem
- Angle Bisector Theorem
- Properties of inequalities of sides and angles of a triangle
- Similarity of Triangles (Corresponding Sides & Angles)
