Height Is Not a Side
Part of the Triangles section of Coddy's Geometry journey. Lesson 18 of 63.
The height of a triangle is not one of its slanted sides. It is the straight drop from a corner to the line of the opposite side, meeting it at a right angle. Usually it falls inside the triangle, but it does not have to.
In this obtuse triangle the corner C hangs past the end of the base AB. The height from C drops down to the line of AB extended, at D, outside the triangle. The dashed extension BD is only there to show where the height lands. The area is still half the base AB times the height CD.
A slanted side is always longer than the height, so using it by mistake makes the area too big. In a right triangle, though, one leg stands at right angles to the other: there the height is a side.
Challenge
△ABC is obtuse. Tap the height that goes with the base AB, then press Check.
Try it yourself
Find the right part on the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles4Area of a Triangle
Half the RectangleHeight Is Not a SideRight Triangle AreaFinding the HeightAny Side Can Be the BaseRecap: Area2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe FormulaRecap: The Third Side5The Pythagorean Theorem
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterSides as ExpressionsRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg