Triangle - Right Triangles

Definition: In geometry, a triangle is a 2-dimensional figure with three sides.

Definition: A right-triangle is a triangle with a right angle (90° angle)

Interactivity 1: Right triangle Directions for interactivity

Click and drag blue points in construction to move and rotate.

Click and drag blue endpoints of base and height line to resize triangle.

Basic formulas for triangles.

Examples with perimeter and area of right-triangles

Base: a	Height: b	Hypotenuse: c = \sqrt{a^2+b^2}	Perimeter: L=a+b+c	Area: A=ab
3 \,cm	4 \,cm	c = \sqrt{3^2\,cm^2+4^2\,cm^2}=\sqrt{25cm^2}=5\,cm	3+4+5 \,cm=12\,cm	3 \,cm \cdot 4 \,cm=12 \,cm^2

Interactivity 2: Construct a right-triangle with the given base and height.

This is a compass and straightedge (compass and ruler) construction.

First, you will need to construct 2 perpendicular lines - Mathcast

Then, using your compass tool, mark out the radius of the base on one perpendicular and the radius of the height on the other.

Equivalent Definitions:

A triangle is a right-triangle if and only if a^2+b^2=c^2 (Pythagoras' theorem is valid).
A right-triangle is determined by the length of any two of its sides and their identity (as non-hypotenuse or hypotenuse).
A right-triangle is determined by the length and identity of a side and an angle.

Theorems

Related themes:

Page last modified on November 06, 2009, at 11:49 PM