Online Geometry: Congruence, Rotation, Translation, Reflection  Page 1




Euclid's Elements
Book I, 23 Definitions. Onepage visual illustration.
Euclid's Elements Book.
Index 

Perpendicular
Bisector. 

Kaleidoscope Index.


Reflection, Theorems and
Problems. 

Euclid's Elements Book I, Proposition 4: (SideAngleSide SAS) 

Geoboard
for iPad Pythagorean Theorem Proof by Leonardo. 

Geoboard
for iPad Pythagorean Theorem Proof, Squares (Problem 540). 

Geoboard
for iPad Gallery: Triangle with two squares (Problem 496). 

Semiperimeter and excircles of a triangle.


Semiperimeter and incircle of a triangle. 

Semiperimeter, incircle and excircles of a triangle.


Parallelogram with Squares theorem Thébault's Theorem.


Johnson's Theorem,
Intersecting circles.
HTML5 Animation 

Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges.


Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.


Langley's Problem
Adventitious angles. 20° isosceles triangle with animation.


Geometry Problem 1577:
Prove that in triangle ABC, segment AB equals the sum of segments BD and CD, with given angles and congruent segments. 

Geometry Problem 1576:
Congruency of Segments in Triangle ABC with Angles 30 and 20 Degrees and an Interior Cevian 

Geometry Problem 1565:
Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence. 

Geometry Problem 1560:
Trapezoid ABCD: Unlocking Angle Secrets at G and H. 

Geometry Problem 1559:
Proving BC Bisects Segment DE. This geometry problem challenges students at high school and college levels. 

Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle. 

Geometry Problem 1557:
Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral,
isosceles, midpoint and congruence 

Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence 

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

Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors 

Geometry Problem 1550: Solving for Segment BD: An Angle Puzzle in Right Triangle ABC: A High School Level Investigation 

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 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 1005030 Degree Angles and Cevian Lengths  A High School Challenge.
. 

Geometry
Problem 1526: Mastering Geometry ProblemSolving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures.
. 

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 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors. 

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 1513 and a Thematic Poem.
Solving the base in a Right Trapezoid with Double Angle and Sum of Two
Sides. Difficulty Level: High School. 

Geometry
Problem 1511 and Poem.
Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School. 

Geometry
Problem 1510 and Poem.
Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School. 

Geometry
Problem 1509 and Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School. 

Geometry
Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular. 

Geometry
Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement. 

Geometry
Problem 1499.
Triangle, Angles, Cevian, Congruence, Isosceles, Equilateral, Auxiliary Construction. 

Geometry
Problem 1496.
Triangle, Congruence, Isosceles, Double Angle, 30 Degrees. 

Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 3060 Degree, Congruence, Auxiliary Lines. 

Dynamic Geometry Problem 1447.
Outer Vecten Point. Stepbystep
illustration using GeoGebra. 

Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Stepbystep animation using GeoGebra. 

Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping. 

Geometry Problem 1429. Triangle, Median, 1530 degree, Angle, Congruence. 

Geometry Problem 1428. Intersecting Circles, Tangent Line, Triangle, Square, Area. 

Geometry Problem 1406. Four Congruent Circles, Measurement, Metric Relations,
Sum of the Squares. 

Geometry Problem 1405. Four Congruent Circles, Congruent Chords. 

Geometry Problem 1404. Three Circles, Center, Intersecting Points, Collinearity, Congruence. 

Geometry Problem 1403. Quadrilateral, 90 Degree Angle, Perpendicular, Congruence. 

Geometry Problem 1401. Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence. 

Geometry Problem 1389. Triangle, 4012020 degree, Angle, Congruence. 

Geometry Problem 1388. Triangle 406080 degree, Incenter, Congruence. 

Geometry Problem 1382. Circle, Diameter, Radius, Perpendicular, Congruence. 

Geometry Problem 1380. Common
Internal Tangents. Circles, Secant, Congruent Chords. 

Geometry Problem 1379. Common External Tangents. Circles, Secant, Congruent Chords. 

Geometry Problem 1361.
Triangle, Two NinePoint Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps. 

Geometry Problem 1359.
Triangle, Circumcircle, Congruent Angles, Midpoints. 

Geometry Problem 1356.
Quadrilateral, Triangle, Angle, 30 Degrees, Congruence. 

Geometry Problem 1353. Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees. 

Geometry Problem 1349. Three Squares, 90 Degrees, Perpendicular Lines, Diagonal. Math Infographic. 

Geometry Problem 1348. Three Concentric Circles, Equilateral Triangle, Perpendicular Bisector, Congruence. 

Geometry Problem 1347. Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle. 

Geometry Problem 1329.
Two Squares Side by Side, Parallel, Perpendicular, 90 Degrees, Congruence. 

Geometry Problem 1328.
Two Squares Side by Side, Perpendicular, 90 Degrees, Congruence. 

Geometry Problem 1317.
Triangle, Excircle, Chord, Tangent, Midpoint, Arc, Sum of two Segments, Congruence. 

Geometry Problem 1316.
Triangle, Incircle, Tangent, Chord, Midpoint, Sum of two Segments, Congruence. 

Geometry Problem 1315.
Triangle, Incircle, Tangent, Chord, Circle, Congruence. 

Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence. 

Geometry Problem 1313.
Regular Decagon, Pentadecagon, Equilateral Triangle, Congruence. 

Geometry Problem 1304.
Triangle, 120 Degrees, Angle Bisector, Measurement. 

Geometry Problem 1303.
Triangle, 60 Degrees, Angle Bisector, Measurement. 

Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence. 

Geometry Problem 1295.
Right Triangle, Incenter, Incircle, Excenter, Excircle, Congruence, Angle. 

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

Geometry Problem 1291.
Three Squares, Collinear Vertices, Midpoint, Congruence. 

Geometry Problem 1287.
Triangle, 4010040 Degrees, Congruence, Area, Metric Relations, Measurement. 

Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement. 

Geometry Problem 1285.
Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement. 

Geometry Problem 1284.
Two Equilateral Triangle, Midpoint, Congruence. 

Geometry Problem 1278.
Square, 345 Right Triangle, Midpoint. 

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

Geometry Problem 1250.
Cyclic or Inscribed Quadrilateral, Circle, Diameter, Congruence. 

Geometry Problem 1238
Square, Equilateral Triangle, Metric Relations. Mobile Apps. 

Geometry Problem 1237
IMO 2016, Problem 1, Triangle, Congruence, Parallel Lines, Midpoint, Concurrency. 
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