Altitude of a Triangle, Theorems and Problems - Table of Content

Euclid's Elements, Book X, Lemma for Proposition 33
One page visual illustration
Altitude.

Orthocenter Index.
Altitudes.

Orthic Triangle Index.

Triangle Orthocenter (Altitudes) by Folding, Video .
Dynamic Geometry Software: Tabula by Numeracy Works.
Step-by-Step construction, Manipulation, and animation.

Euclid's Elements Book II, Proposition 12: Law of Cosines.
Altitude.

Euclid's Elements Book II, Proposition 13: Law of Cosines.
Altitude.

Right triangle, Altitude, Incircle
Right Triangle, Altitude to the Hypotenuse, Incircle, Incenter, Inradius, Angle Bisector, Theorems and Problems, Index.

GeoGebra, Dynamic Geometry: Orthocenter of a Triangle.
HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Nine Point Circle
HTML5 Animation for Tablets (iPad, Nexus..)

GeoGebra, Dynamic Geometry: Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus..)

Geometry Problem 803
Right Triangle, Altitude, Angle Bisector, Perpendicular, Measurement.

Geometry Problem 796
Triangle, Altitude, Measurement of Angles.

Geometry Problem 794
Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence.

Geometry Problem 793
Right Triangle, Altitude, Three Incircles, Incenters, Circumcircle, Circumradius, Perpendicular, Distance.

Geometry Problem 792
Right Triangle, Altitude, Angle Bisector, Three Incircles, Five Concyclic Points, Circles.

Geometry Problem 790
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line, Congruence.

Geometry Problem 789
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line.

Geometry Problem 784
Triangle, Orthocenter, Altitude, Midpoint of a side, Perpendicular.

Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Midpoint.

Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram.

Geometry Problem 781
Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular.

Geometry Problem 780
Triangle, Sum of Inradius and Circumradius, Distances from the Orthocenter to the Vertices.

Geometry Problem 779
Triangle, Altitude, Orthocenter, Midpoint, Angle, 90 Degrees.

Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.

Geometry Problem 777
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Cosine.

Geometry Problem 766
Triangle, Altitudes, Exradii, Three Exradius, Equal Harmonic Mean.

Geometry Problem 764
Triangle, Inradius, Altitudes, Harmonic Mean.

Geometry Problem 753.
Triangle, Altitudes, Orthocenter, Sum of ratios.

Geometry Problem 736.
Triangle, Altitude, Perpendicular, Angles, Cyclic Quadrilateral.

Geometry Problem 735.
Triangle, Altitude, Perpendicular, Semiperimeter of the Orthic Triangle, Congruence.

Geometry Problem 733.
Triangle, Orthocenter, Altitude, Reflection in a line, Circumcircle, Concurrency.

Geometry Problem 732.
Triangle, Altitude, Orthic Triangle, Orthocenter, Congruence, Parallelogram.

Geometry Problem 731.
Cyclic quadrilateral, Triangle, Orthocenter, Altitude, Perpendicular, Parallelogram.

Geometry Problem 730.
Triangle, Altitude, Orthocenter, Perpendicular, Concurrent Lines.

Geometry Problem 729.
Triangle, Altitude, Orthocenter, Circumcircle, Perpendicular, Midpoint.

Geometry Problem 728.
Triangle, Altitude, Perpendicular, Circumcircle, Midpoint, Intersecting Circles, Concurrency.

Geometry Problem 726.
Isosceles Triangle, Perpendicular, Altitude, Midpoint, 90 Degrees.

Geometry Problem 721.
Triangle, Orthocenter, Circumcircle, Altitude, Collinear points, Altitude.

Geometry Problem 715.
Triangle, Altitudes, Parallel, Circumcircle, Angle, Measurement.

Geometry Problem 704.
Triangle, Orthocenter, Altitude, Midpoint, Perpendicular.

Geometry Problem 678.
Triangle, Altitude, Simson Line, Circumcircle, Tangent, Parallel, Perpendicular, Collinear Points.

Geometry Problem 674.
Triangle, Altitude, Angles.

Geometry Problem 663.
Scalene Triangle, 60 Degrees, Altitude, Angle Bisector, Perpendicular Bisector.

Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles.

Geometry Problem 634
Right Triangle, Altitude, Incenters, Areas.

Geometry Problem 629
Triangle, Perpendicular to Sides, Intersecting Lines, Altitude.

Geometry Problem 613
Altitude of a Triangle, Perpendicular, Collinear Points.

Geometry Problem 612
Altitude of a Triangle, Perpendicular, Congruence.

Geometry Problem 611
Altitude of a Triangle, Perpendicular, Collinear Points, Parallel.

Geometry Problem 594.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude, Angle, Half the Difference.

Geometry Problem 591.
Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude.

Problem 515.
Triangle, Double Angle, Altitude, Measure.

Proposed Problem 427.
Triangle, Two Altitudes, Square of a Side.

Proposed Problem 420.
Triangle, Altitude, Angles, Sides, Measurement.

Proposed Problem 414.
Triangle, Angles, Altitude, Median, Congruence.

Proposed Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence.

Proposed Problem 397.
Triangle, Altitude, Midpoints, Congruence.

Proposed Problem 393.
Triangle, Orthocenter, Altitude, Circumcircles, Congruence, Collinear.

Proposed Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points.

Proposed Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points.

Proposed Problem 325.
Isosceles triangle, Altitude, Cevian, Incircle, Excircle.

Proposed Problem 321.
Triangle, Incenter, Excircle, Midpoint of the Altitude, Collinearity.

Proposed Problem 319.
Triangle, Altitudes, Perpendiculars, Collinear points.

Proposed Problem 318.
A Scalene triangle, Altitudes, Collinear points.

Arithmetic Mean, Geometric Mean, Harmonic Mean, Root Mean Square.
Altitude of a right triangle.

Proposed Problem 269.
Right Triangle, Altitude, Perpendicular, Projection.

Proposed Problem 268.
Right Triangle, Catheti and Altitude.

Proposed Problem 266.
Right Triangle, Altitude, Geometric Mean.

Proposed Problem 264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean.

Proposed Problem 263.
Triangle, Median, Altitude, Orthogonal Projection, Sides.

Proposed Problem 222. Viviani's theorem, Equilateral triangle, Exterior point, Distances, Altitude.  

Proposed Problem 221. Viviani's theorem, Equilateral triangle, Interior point, Distances, Altitude.  

Proposed Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.  

Proposed Problem 218. Right triangle, Altitude and Projections.

Proposed Problem 217. Right triangle, Altitude and Projections.

Proposed Problem 199. Triangle, Altitude, Quadrilateral, Angles.

Proposed Problem 191. Triangle, Altitudes, Orthocenter, Squares, Areas.

Proposed Problem 187. Right Triangle, Altitude, Incenters, Circles, Angles.  

Proposed Problem 186. Right Triangle, Altitude, Incenters, Circles.  

Proposed Problem 186. Right Triangle, Altitude, Incenters, Circles.  

Proposed Problem 139. Triangle Area, Altitudes, Orthic Triangle, Semiperimeter, Circumradius.  

Proposed Problem 138. Nagel's Theorem, Altitudes, Orthic Triangle, Circumradius, Perpendicular.  

Proposed Problem 137. Orthic Triangle, Altitudes, Perpendicular, Incircle, Collinear Points, Parallelogram.  

Proposed Problem 136. Orthic Triangle, Altitudes, Perpendicular, Concyclic Points.  

Proposed Problem 135. Orthic Triangle, Altitudes, Perpendicular, Parallel  

Proposed Problem 134. Orthic Triangle, Altitudes, Angle Bisectors, Orthocenter, Incenter.  

Proposed Problem 91. Similar Triangles, Altitudes, Parallel.

Taylor Circle Theorem Feet of each altitude.
Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Henry Martyn Taylor and the blind student of mathematics

Proposed Problem 79: Triangle. Similarity, Altitudes, Orthocenter, Incircles, Inradii.

Proposed Problem 70: Squares inscribed in a triangle, Similarity. Altitude.

Proposed Problem 69: Square inscribed in a triangle, Similarity. Altitude.

Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.

Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.
Altitudes, Orthocenter.

Geometry Problem 800: de Gua's Theorem
Pythagorean theorem in 3-D, Tetrahedron, Cubic Vertex, Triangular Pyramid, Apex, Height, Right Triangle Area, Base Area, Projected Area.

Triangle and Squares 22
Altitudes 

Proposed Problem 51: Fagnano's Problem
Inscribed Triangle with the Minimum Perimeter.
Altitudes.

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean, hypotenuse, catheti (legs), semiperimeter, altitude, median, similar shapes areas, centers, orthocenter, incenter, centroid, circumcenter, radius, inradius, circumradius, exradius, circles, incircle, circumcircle, excircle.

Triangle and Squares 20
Altitude.

Proposed Problem 49. Right triangle, Altitude, Angles.

Blanchet Theorem
Altitude.

Proposed Problem 29.
Right Triangle, altitude, incircle and inradius. Ten conclusions.

Proposed Problem 28
Right Triangle, altitude, incircles and inradius.

Proposed Problem 26
Right Triangle, altitude, incircles and inradius.

Proposed Problem 25
Right Triangle, altitude, incircles and inradius.

Proposed Problem 24
Right Triangle, altitude, incircles and inradii.

Proposed Problem 23
Right Triangle, altitude, incircles and inradii.

Proposed Problem 22
Right Triangle, altitude, incircles and inradii.

Proposed problem 21
Acute triangle, altitudes, orthocenter, diameter, tangents.

Proposed problem 20
Right Triangle, altitude, incircles and inradii.

Triangle and Squares 5
Altitude and median.

Triangle and Squares 3
Altitude.

Geometry Online Glossary. Altitude.
Geometry Glossary based on the new New York State mathematics standards initiative.

Interactive Geometry Glossary using AnswerTips technology.
Altitude.