Altitude of a Triangle, Theorems and Problems - Table of Content 1

Altitude, so high,
Triangle's perpendicular,
Theorems come alive.
Problems unravel with ease,
Altitude unveils secrets.

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

Orthocenter Index.
Altitudes.

Orthic Triangle Index.

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..)

Geometry Problem 1575: Prove an Angle Bisector in a Triangle Involving an Altitude, Midpoint, and Excircle

Geometry Problem 1564: Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints.

Geometry Problem 1563: Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints.

Geometry Problem 1562: Proof of Collinearity in a Right-angled Triangle involving the Altitude, Angle bisectors, and Midpoint.

Geometry Problem 1561: Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle Secrets.

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

Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC

Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes

Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!.

Geometry Problem 1523 and a Thematic Poem.
Discover How to Calculate the Length of the Altitude in an Isosceles Triangle - Get Expert Geometry Tips Now! .

Geometry Problem 1507.
Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School.

Geometry Problem 1492.
Right Triangle, Altitude, Incenters, Angle, Measurement.

Geometry Problem 1488.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1487.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1486.
Right Triangle, Altitude, Incircle, Tangent, Measurement.

Geometry Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement.

Geometry Problem 1484.
Right Triangle, Altitude, Incircles, Inradius, Measurement.

Dynamic Geometry 1476.
Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra, iPad.

Geometry Problem 1459.
Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration using GeoGebra.

Geometry Problem 1457.
Altitudes, Circles, Similarity, Product of the Inradii Lengths, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1456.
Altitudes, Orthic Triangle, Circumcircle, Parallel lines, Similarity, Area, iPad. Step-by-step illustration using GeoGebra.

Geometry Problem 1442.
Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement, Art, Poster, Typography, iPad Apps.

Geometry Problem 1436.
Right Triangle, Altitude, Excircles, Excenters, Geometric Mean, Measurement, Art, Poster, Typography, iPad Apps.

Geometry Problem 1416.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Geometry Problem 1415.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Geometry Problem 1414.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Geometry Problem 1375.
Isosceles Triangle, Interior Cevian, Exradius, Excircle, Altitude to the Base.

Geometry Problem 1373.
Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude to the Base.

Geometry Problem 1346.
Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance.

Geometry Problem 1312.
Triangle, 60 Degrees, Circle, Circumcenter, Orthocenter, Altitude, Distance, Perpendicular, Measurement.

Geometry Problem 1294.
Triangle, Altitudes, Four Squares, Center, Midpoint, Concyclic Points.

Geometry Problem 1293.
Triangle, Altitudes, Two Squares, Center, Concurrent Lines, Midpoint.

Geometry Problem 1281.
Triangle, Circle, Diameter, Tangent, Altitude, Congruent Angles.

Geometry Problem 1272.
Isosceles Triangle, Median, Midpoint, Perpendicular, 90 Degrees, Angles, Congruence.

Geometry Problem 1262.
Isosceles Triangle, Altitude, Medians, 90 Degrees, Perpendicular.

Geometry Problem 1257.
Triangle, Altitude, Perpendicular, 90 Degree, Measurement.

Geometry Problem 1253.
Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency.

Geometry Problem 1252.
Triangle, Circle, Circumcircle, Altitude, Area, Hexagon, Perpendicular, 90 Degrees. Mind Map.

Geometry Problem 1248.
Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines.

Geometry Problem 1247.
Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Midpoint.

Geometry Problem 1246.
Triangle, Orthocenter, Altitude, Midpoint, Perpendicular.

Geometry Problem 1233
Triangle, Euler Line, Orthic Axis, Perpendicular, 90 Degrees, Orthic Triangle.

Geometry Problem 1232
Triangle, Altitudes, Orthic Triangle, Collinearity, Orthic Axis.

Geometry Problem 1213
Triangle, Circumcircle, Altitudes, Cyclic Quadrilateral, Congruence.

Geometry Problem 1211
Right Triangle, Altitude, Angle Bisector, 45 Degrees.

Geometry Problem 1199
Equilateral Triangle, Square, Altitude, Circle, Incircle, Inradius, Metric Relations.

Geometry Problem 1171
Area of a Triangle in terms of the three altitude or heights h_a, h_b, h_c.

Geometry Problem 1170
Area of a Triangle in terms of the three sides, a-b-c.

Geometry Problem 1169
Complete Quadrilateral, Orthocenters of the Component Triangles, Collinear Points, Ortholine, Steiner-line, Orthocentric line.

Geometry Problem 1155.
Right Triangle, Altitude, Incenter, Incircle, Area.

Geometry Problem 1150.
Circle, Perpendicular Secants, 90 Degrees, Congruence.

Geometry Problem 1149.
Isosceles Triangle, Altitude, Cevian, Incircles, Tangent, Congruence.

Geometry Problem 1073.
Triangle, Altitudes, Exterior Point, Distance, Ratio.

Geometry Problem 1072.
Triangle, Altitudes, Interior Point, Distance, Ratio.

Geometry Problem 1068.
Obtuse Triangle, Orthocenter, Circumradius, Inradius, Exradii, Distance, Diameter

Geometry Problem 1067.
Acute Triangle, Orthocenter, Circumradius, Inradius, Exradii, Distance, Diameter.

Geometry Problem 1066.
Triangle, Obtuse Angle, Orthocenter, Circumradius R, Inradius r, Exradius r_a, Distance, Diameter.

Geometry Problem 1065.
Triangle, Acute Angle, Orthocenter, Circumradius R, Inradius r, Exradius r_a, Distance, Diameter.

Geometry Problem 1064.
Triangle, Orthocenter, Altitudes, Circumradius, Sum of the Squares of Sides.

Geometry Problem 1063.
Triangle, Orthocenter, Altitudes, Equal Product of the Lengths of Segments.

Geometry Problem 1059.
Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Reflection of a Point over a Line, Collinear Points, Simson Line, Congruence.

Geometry Problem 1058.
Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter.

Geometry Problem 1056.
Triangle, Exradius, Reciprocals of the Altitudes, Multiplicative Inverse, Perpendicular, Excircle, Circle.

Geometry Problem 1055.
Triangle, Altitude, Perpendicular, Area, Circumradius, Circle.

Geometry Problem 1054.
Triangle, Altitude, Orthocenter, Circumcenter, Perpendicular, Midpoints.

Geometry Problem 1016.
Triangle, 45 Degrees, Area, Triangle, Quadrilateral, Altitude, Bisector.

Geometry Problem 1015.
Right Triangle, Square, Altitude, Metric Relations.

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