Geometry: Congruence, Rotation, Translation, Reflection

Geometry Problem 1607: Circle, Chords, Tangents, 60 Degree Angle

Geometry Problem 1606: Nested Squares Area Challenge

Geometry Problem 1599: Four Equal Squares, One Right Triangle: What’s the Ratio?: A STEM Geometry Challenge

Geometry Problem 1598: Inradius Ratio with Median BM in a Right-Angled Triangle: A STEM Geometry Challenge

Geometry Problem 1597: Circle-Triangle Intersection Problem: A STEM Geometry Challenge

Geometry Problem 1596: Triangle Projections: Unraveling the DE Projection with Equal Angles!: A STEM Geometry Challenge

Geometry Problem 1594: Intersecting Squares & Hidden Lengths – A STEM Perspective

Geometry Problem 1593: Find BF in Right Triangle ABC – A STEM Perspective

Geometry Problem 1592: A Semicircle Challenge for Mental Clarity Involving Radii, Perpendiculars, Midpoint

Geometry Problem 1591: Unravel Quadrilateral ABCD with Three Congruent Sides and Proportional Angles to Find Angle D.

Geometry Problem 1590: Midpoints, Incircles, Areas, and the Art of Balance.

Euclid's Elements Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book. Index

Perpendicular Bisector.

Kaleidoscope Index.

Reflection, Theorems and Problems.

Euclid's Elements Book I, Proposition 4: (Side-Angle-Side 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 1589: Unlock the Mystery: Prove the Ratio of BD to OD is Square Root of Two in a 90° Circular Sector!.

Geometry Problem 1588: Unlocking the Tangent: Prove the Fifth of the Radius in a Sector with Semicircle.

Geometry Problem 1586: Unveiling a Unique Area Relationship in Three Equilateral Triangles

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 100-50-30 Degree Angles and Cevian Lengths - A High School Challenge.
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Geometry Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures.
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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, 30-60 Degree, Congruence, Auxiliary Lines.

Dynamic Geometry Problem 1447.
Outer Vecten Point. Step-by-step illustration using GeoGebra.

Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra.

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

Geometry Problem 1429.
Triangle, Median, 15-30 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, 40-120-20 degree, Angle, Congruence.

Geometry Problem 1388.
Triangle 40-60-80 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 Nine-Point 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.

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