![Midpoint Index](midpoint_index_17.jpg) |
|
![Point, Theorems and Problems, Index](point_theorems_index_17.jpg) |
Points, Theorems and Problems - Index.
|
![Perpendicular Bisector Index](../math_geometry_online_courses/perpendicular_bisector_i_1.jpg) |
Perpendicular
Bisector. |
![](../butterfly_theorem_170x100.jpg) |
Butterfly Theorem
Proof with animation.
Midpoint of a chord. |
![Trapezoid median, Theorems and Problems, Index](trapezoid_median_index_17.jpg) |
Median of a Trapezoid, Theorems and Problems.
Index.
|
![](../NewtonTheorem170.jpg) |
Newton's
Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of
diagonals, center of the circle inscribed.
|
![Dynamic Geometry: Nine Point Circle. HTML5 Animation for Tablets (iPad, Nexus..)](../geogebra/nine-point-circle-euler-feuerbach-html5-animation-ipad-nexus-1.jpg) |
GeoGebra, Dynamic Geometry:
Nine Point Circle
HTML5 Animation for Tablets (iPad, Nexus..) |
![Dynamic Geometry: Internal Feuerbach Point. HTML5 Animation for Tablets iPad, Nexus](../geogebra/internal-feuerbach-point-html5-animation-tablet-ipad-nexus-1.jpg) |
GeoGebra, Dynamic Geometry:
Internal Feuerbach Point
HTML5 Animation for Tablets (iPad, Nexus..) |
![](../equilic_quadrilateral_170.jpg) |
Equilic Quadrilateral.
120 degrees. Midpoints. |
![](../Kurschak170x100.jpg) |
Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.
Midpoints. |
![](../Varignon_Wittenbauer_170.jpg) |
Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges.
|
![Median Length theorem](median_length_17.jpg) |
Median
length, Apollonius' Theorem
Midpoints. |
![Van Aubel](../vanaubel170x100.jpg) |
Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
Midpoints. |
![](../center/lemoine_point_170.jpg) |
Symmedian (Lemoine)
Point
Triangle Center |
![](../ArchBooLem07_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 7
Square and inscribed and circumscribed Circles Midpoints.
|
![](../ArchBooLem02_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 2
Semicircle, diameter, tangents, secant line.
Midpoint. |
![](../ArchBooLem03_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 3
Semicircle, perpendicular to diameter, chords.
Midpoint. |
![](../ArchBooLem10_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 10
Tangents to a circle, secant line and chords, Parallel.
Midpoint. |
![](../ArchBooLem15_170.jpg) |
Archimedes' Book of Lemmas:
Proposition 15
Circle, Diameter, Inscribed Regular Pentagon, Arc, Midpoint,
Perpendicular, Radius. |
![Bottema Theorem. Elearning.](bottema_theorem_elearning.jpg) |
Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation.
Midpoints. |
![Eight Point Circle Theorem. Elearning](eight_point_circle_17.jpg) |
Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.
Perpendiculars from the midpoints. |
![](marion_walter_theorem.jpg) |
Marion
Walter's Theorem: Triangle and Hexagon areas:
Using TracenPoche Dynamic Geometry Software.
Midpoints. |
![](../center/nine_point_center_euler_170.jpg) |
Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.
|
![](../circle/mascheroni_construction_1.jpg) |
Mascheroni
Construction with compass alone. Midpoint of a segment.
|
![](../heron/heron_medians_170x100.jpg) |
Heron's Formula with medians.
Midpoints. |
![](../center/mittenpunkt_point_170.jpg) |
Mittenpunkt Point
Midpoints. |
![Brahmagupta's Theorem](../software/dynamic-geometry-brahmagupta-theorem-cyclic-quadrilateral-ipad-1.jpg) |
Dynamic Geometry: Brahmagupta Theorem,
. GeoGebra, HTML5 Animation for Tablets |
![Geometry Problem 1563](../school-college/6/p1563-midpoint-mysteries-proving-perpendicularity-in-right-triangle-abc-altitude-bisectors-1.jpg) |
Geometry Problem 1563:
Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. |
![Geometry Problem 1562](../school-college/6/p1562-right-angled-triangle-bisector-midpoint-collinear-points-proof-1.jpg) |
Geometry Problem 1562:
Proof of Collinearity in a Right-angled Triangle involving the Altitude, Angle bisectors, and Midpoint. |
![Geometry Problem 1560](../school-college/6/p1560-trapezoid-ABCD-geometry-puzzle-angles-G-and-H-AGD-50-degrees-1.jpg) |
Geometry Problem 1560:
Trapezoid ABCD: Unlocking Angle Secrets at G and H. |
![Geometry Problem 1559](../school-college/6/p1559-high-school-geometry-problem-ABC-triangle-bisection-angles-proof-1.jpg) |
Geometry Problem 1559:
Proving BC Bisects Segment DE. This geometry problem challenges students at high school and college levels. |
![Geometry Problem 1558](../school-college/6/p1558-midpoints-of-segments-connecting-corresponding-vertices-of-two-equilateral-triangles-form-an-equilateral-triangle-1.jpg) |
Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle. |
![Geometry Problem 1557](../school-college/6/p1557-right-triangle-equilateral-isosceles-congruence-midpoint-angle-problem-solving-1.jpg) |
Geometry Problem 1557:
Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral,
isosceles, midpoint and congruence |
![Geometry Problem 1554](../school-college/6/p1554-triangle-ABC-angles-A-B-altitude-AH-median-AM-length-HM-4-units-length-AB-1.jpg) |
Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC |
![Geometry Problem 1553](../school-college/6/p1553-triangle-abc-angle-bisectors-calculate-circumradius-1.jpg) |
Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors |
![Geometry Problem 1548](../school-college/6/p1548-triangle-abc-angle-a-45-altitudes-bd-ce-intersect-point-f-de-length-calculation-1.jpg) |
Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes |
![Geometry Problem 1543](../school-college/6/p1543-square-circle-arc-mindpoint-quadrilateral-area-school-college-1.jpg) |
Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc. |
![Geometry Problem 1539](../school-college/6/p1539-isosceles-triangle-tangent-circle-altitude-right-angle-midpoint-measurement-math-class-1.jpg) |
Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!. |
![Geometry Problem 1538](../school-college/6/p1538-triangle-external-squares-quadrilateral-area-segment-length-math-class-1.jpg) |
Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length. |
![Geometry Problem 1537](../school-college/6/p1537-parallelogram-midpoint-triangle-area-intersection-math-challenge-1.jpg) |
Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?. |
![Geometry Problem 1536](../school-college/6/p1536-quadrilateral-midpoint-area-triangle-math-education-1.jpg) |
Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. |
![Geometry Problem 1525](../school-college/6/p1525-right-triangle-equilateral-midpoint-hypotenuse-distance-1.jpg) |
Geometry
Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. |
![Geometry Problem 1524](../school-college/6/p1524-parallelogram-angle-bisector-intersect-distance-1.jpg) |
Geometry
Problem 1524 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors. |
![Geometry Problem 1523](../school-college/6/p1523-calculate-length-altitude-isosceles-triangle-midpoint-1.jpg) |
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 1522](../school-college/6/p1522-triangle-median-double-angle-side-geometry-poem-1.jpg) |
Geometry
Problem 1522 and a Thematic Poem.
Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths. |
![Geometry Problem 1519](../school-college/6/p1519-parallelogram-length-midpoints-parallel-line-1.jpg) |
Geometry
Problem 1519 and a Thematic Poem.
Discover the Length of a Segment in a Parallelogram using Midpoints and Parallel Lines. |
![Geometry Problem 1517](../school-college/6/p1517-unlock-triangle-side-length-solving-median-angles-1.jpg) |
Geometry
Problem 1517 and a Thematic Poem.
Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School. |
![Geometry Problem 1515](../school-college/6/p1515-distance-centroid-triangle-median-exterior-line-perpendicular-1.jpg) |
Geometry
Problem 1515 and a Thematic Poem.
Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line. Difficulty Level: High School. |
![Geometry Problem 1512](../school-college/6/p1512-triangle-median-cevian-given-ratio-midpoint-midline-theorem-poem-1.jpg) |
Geometry
Problem 1512 and a Thematic Poem.
Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School. |
![Geometry Problem 1494](../school-college/5/p1494-parallelogram-midpoints-octagon-area-1.jpg) |
Geometry
Problem 1494.
Parallelogram, Midpoints, Octagon, Areas. |
![Dynamic Geometry 1476](../school-college/5/p1476-droz-farny-line-theorem-orthocenter-collinear-midpoint-geogebra-1.jpg) |
Dynamic Geometry 1476.
Droz-Farny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1474](../school-college/5/p1474-butterfly-theorem-circle-chord-midpoint-geogebra-ipad-1.jpg) |
Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration. |
![Dynamic Geometry 1469](../school-college/5/p1469-triangle-inradius-circumradius-midpoint-geogebra-1.jpg) |
Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Step-by-step Illustration. |
![Geometry Problem 1466](../school-college/5/p1466-tangential-quadrilateral-newton-line-incenter-geogebra-ipad-1.jpg) |
Geometry Problem 1466.
Tangential Quadrilateral, Newton Line, Incenter, Midpoint, Diagonal, Collinear Points.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1464](../school-college/5/p1464-quadrilateral-midpoint-equal-sum-area-1.jpg) |
Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas.
Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1461](../school-college/5/p1462-newton-theorem-gauss-line-quadrilateral-midpoint-side-diagonal-geogebra-1.jpg) |
Geometry Problem 1462.
Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals,
Collinear Points. |
![Geometry Problem 1460](../school-college/5/p1460-newton-gauss-line-dynamic-complete-quadrilateral-1.jpg) |
Dynamic Geometry
1460.
Newton-Gauss Line, Complete Quadrilateral, Midpoints of Diagonals,
Collinear Points, Step-by-step Illustration using GeoGebra. |
![Geometry Problem 1459](../school-college/5/p1459-orthocenter-triangle-midpoint-perpendicular-1.jpg) |
Geometry
Problem 1459.
Two Triangles, Orthocenter, Midpoint, Perpendicular, Step-by-step Illustration using GeoGebra. |
![Problem 1444](../school-college/5/p1444-asymmetric-propeller-equilateral-triangle-geogebra-1.jpg) |
Dynamic Geometry Problem 1444.
The Asymmetric Propeller Theorem, Equilateral Triangles, Midpoints. Using GeoGebra. |
![Problem 1429](../school-college/5/p1429-triangle-median-angle-15-30-degree-1.jpg) |
Geometry Problem 1429. Triangle, Median, 15-30 degree, Angle, Congruence. |
![Problem 1417](../school-college/5/p1417-triangle-incenter-circumcircle-tangent-cevian-bisector-perpendicular-1.jpg) |
Geometry Problem 1417. Triangle, Cevian, Circumcircle, Incenter, Perpendicular, Angle Bisector,
Tangent Lines, Tangent Circles, Midpoint. |
![Problem 1408](../school-college/5/p1408-right-triangle-incircle-excircle-midpoint-collinear-1.jpg) |
Geometry Problem 1408. Right Triangle, Incircle, Excircle, Incenter, Midpoint, Tangency Point, Collinearity. |
![Problem 1395](../school-college/4/p1395-triangle-rectangles-midpoints-concurrency-1.jpg) |
Geometry Problem 1395. Triangle with three rectangles on the sides, Midpoints, Perpendicular lines, Concurrency. |
![Problem 1388 Circle, Triangle](../school-college/4/p1385-triangle-circumcircle-orthocenter-bisector-collinear-1.jpg) |
Geometry Problem 1385. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points. |
![Geometry problem 1365](../school-college/4/p1365-circle-chord-parallel-secant-tangent-midpoint-1.jpg) |
Geometry Problem 1365.
Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad Apps. |
![Geometry problem 1360](../school-college/4/p1360-nine-point-circle-euler-cyclic-tutor-sketch-sw-1.jpg) |
Geometry Problem 1360.
Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps. |
![Geometry problem 1359](../school-college/4/p1359-triangle-circumcircle-equal-angle-midpoint-tutor-1.jpg) |
Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints. |
![Geometry problem 1355](../school-college/4/p1355-triangle-median-circle-measurement-tutoring-1.jpg) |
Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure of segments. |
![Geometry problem 1351](../school-college/4/p1351-circumscribed-tangential-quadrilateral-midpoint-perpendicular-1.jpg) |
Geometry Problem 1351. Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars. |
![Geometry problem 1342](../school-college/4/p1342-circle-chord-secant-parallel-midpoint-cyclic-1.jpg) |
Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.
|
![Geometry problem 1336](../school-college/4/p1336-right-triangle-double-angle-90-degrees-tutoring-1.jpg) |
Problem 1336.
Right Triangle, Cevian, Double Angle, Perpendicular, 90 Degrees.
|
![Geometry problem 1325](../school-college/4/p1325-octagon-midpoint-square-math-education-1.jpg) |
Geometry Problem 1325.
Octagons, Midpoints, Squares, Mobile Apps, iPad. |
![Geometry problem 1317](../school-college/4/p1317-triangle-excircle-tangent-chord-congruence-1.jpg) |
Geometry Problem 1317.
Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence. |
![Geometry problem 1316](../school-college/4/p1316-triangle-incircle-chord-sum-segment-congruence-1.jpg) |
Geometry Problem 1316.
Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence. |
![Geometry problem 1302](../school-college/4/p1302-triangle-median-circle-congruence-1.jpg) |
Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence. |
![Geometry problem 1301](../school-college/4/p1301-arbelos-incircle-square-midpoint-1.jpg) |
Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. |
![Geometry problem 1298](../school-college/3/p1298-arbelos-incircle-angle-bisector-perpendicular-midpoint-1.jpg) |
Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint. |
![Geometry problem 1294](../school-college/3/p1294-triangle-square-altitude-circle-geometry-1.jpg) |
Geometry Problem 1294.
Triangle, Altitudes, Four Squares, Center, Midpoint, Concyclic Points. |
![Geometry problem 1293](../school-college/3/p1293-triangle-square-altitude-concurrent-1.jpg) |
Geometry Problem 1293.
Triangle, Altitudes, Two Squares, Center, Concurrent Lines, Midpoint. |
![Geometry problem 1291](../school-college/3/p1291-three-squares-midpoint-collinear-1.jpg) |
Geometry Problem 1291.
Three Squares, Collinear Vertices, Midpoint, Congruence. |
Go to Page: Previous |
1 |
2 |
3
| 4
| 5
| 6
| 7
| 8
| 9
| 10 |
Next
|