Online Geometry: Congruence, Rotation, Translation, Reflection - Page 1
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![Congruence, Translation, Rotation, Reflection](congruence_geometry_17.jpg) |
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![Euclid's Elements 23 definitions](euclid_elements_definition_170.jpg) |
Euclid's Elements
Book I, 23 Definitions. One-page visual illustration.
Euclid's Elements Book.
Index |
![Perpendicular Bisector Index](../math_geometry_online_courses/perpendicular_bisector_i_1.jpg) |
Perpendicular
Bisector. |
![Kaleidoscope Index](../geometric_art/kaleidoscope_17.jpg) |
Kaleidoscope Index.
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![Reflection Index](reflection/reflection-theorem-problem-index-1.jpg) |
Reflection, Theorems and
Problems. |
![a](euclid_book_i_4_sas_17.jpg) |
Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS) |
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Geoboard
for iPad Pythagorean Theorem Proof by Leonardo. |
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Geoboard
for iPad Pythagorean Theorem Proof, Squares (Problem 540). |
![iPadd Apps Geoboard, triangle with two squares](../geoboard/ipad-geoboard-496-triangle-squares-1.jpg) |
Geoboard
for iPad Gallery: Triangle with two squares (Problem 496). |
![](../semiperimeter_excircle170.jpg) |
Semiperimeter and excircles of a triangle.
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![](../semiperimeter_incircle170.jpg) |
Semiperimeter and incircle of a triangle. |
![](../semiperimeter_in_exc170.jpg) |
Semiperimeter, incircle and excircles of a triangle.
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![](../parallelogramsquare170x100.jpg) |
Parallelogram with Squares theorem Thébault's Theorem.
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![Johnson: Intersecting circles](../geometry/johnson-theorem-four-circles-html5-1.jpg)
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Johnson's Theorem,
Intersecting circles.
HTML5 Animation |
![](../Varignon_Wittenbauer_170.jpg) |
Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges.
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![Van Aubel](../vanaubel170x100.jpg) |
Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
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![](../langley170x100.jpg) |
Langley's Problem
Adventitious angles. 20° isosceles triangle with animation.
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![Geometry Problem 1565](../school-college/6/p1565-triangle-median-perpendicular-midpoint-congruence-tutoring-1.jpg) |
Geometry Problem 1565:
Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence. |
![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 1556](../school-college/6/p1556-right-triangle-inscribed-circle-properties-and-length-of-FG-problem-solving-1.jpg) |
Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, 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 1550](../school-college/6/p1550-right-triangle-angle-based-segment-length-calculation-isosceles-congruence-1.jpg) |
Geometry Problem 1550: Solving for Segment BD: An Angle Puzzle in Right Triangle ABC: A High School Level Investigation |
![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 1529](../school-college/6/p1529-triangle-interior-cevian-30-100-degree-congruence-find-missing-angle-1.jpg) |
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](../school-college/6/p1526-parallelogram-intersecting-bisectors-distance-congruence-1.jpg) |
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](../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!
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![Geometry Problem 1513](../school-college/6/p1513-right-trapezoid-solving-base-double-angle-sum-two-sides-thematic-poem-1.jpg) |
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](../school-college/6/p1511-isosceles-triangle-point-on-the-extensionof-base-distance-measurement-altitude-congruence-poem-1.jpg) |
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](../school-college/6/p1510-three-triangle-congruence-perimeter-measurement-poem-1.jpg) |
Geometry
Problem 1510 and Poem.
Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School. |
![Geometry Problem 1509](../school-college/6/p1509-square-trapezoid-congruence-measurement-1.jpg) |
Geometry
Problem 1509 and Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School. |
![Geometry Problem 1503](../school-college/6/p1503-triangle-transversal-line-tangent-incircle-distance-vertices-perpendicular-congruence-1.jpg) |
Geometry
Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular. |
![Geometry Problem 1501](../school-college/6/p1501-square-interior-point-distance-equal-angles-measurement-1.jpg) |
Geometry
Problem 1501.
Square, Exterior Point, Congruent Angles, Segment, Measurement. |
![Geometry Problem 1498](../school-college/5/p1499-triangle-angle-congruence-cevian-1.jpg) |
Geometry
Problem 1499.
Triangle, Angles, Cevian, Congruence, Isosceles, Equilateral, Auxiliary Construction. |
![Geometry Problem 1496](../school-college/5/p1496-triangle-double-angle-isosceles-30-degree-congruence-1.jpg) |
Geometry
Problem 1496.
Triangle, Congruence, Isosceles, Double Angle, 30 Degrees. |
![Geometry Problem 1461](../school-college/5/p1461-quadrilateral-angle-30-congruence-1.jpg) |
Geometry Problem 1461.
Quadrilateral, Triangle, Angles, 30-60 Degree, Congruence, Auxiliary Lines. |
![Problem 1447](../school-college/5/p1447-vecten-point-outer-geogebra-dynamic-1.jpg) |
Dynamic Geometry Problem 1447.
Outer Vecten Point. Step-by-step
illustration using GeoGebra. |
![Problem 1445](../school-college/5/p1445-van-aubel-theorem-quadrilateral-geogebra-step-1.jpg) |
Dynamic Geometry Problem 1445.
Van Aubel's theorem, Quadrilateral and Four Squares, Centers. Step-by-step animation using GeoGebra. |
![Problem 1431](../school-college/5/p1431-apollonius-llc-triangle-circumcircle-tangent-congruent-angle-1.jpg) |
Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping. |
![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 1428](../school-college/5/p1428-circle-tangent-triangle-square-area-1.jpg) |
Geometry Problem 1428. Intersecting Circles, Tangent Line, Triangle, Square, Area. |
![Problem 1406](../school-college/5/p1406-four-congruent-circles-measurement-tutor-1.jpg) |
Geometry Problem 1406. Four Congruent Circles, Measurement, Metric Relations,
Sum of the Squares. |
![Problem 1405](../school-college/5/p1405-four-congruent-circles-chords-tutor-1.jpg) |
Geometry Problem 1405. Four Congruent Circles, Congruent Chords. |
![Problem 1404](../school-college/5/p1404-three-circles-congruence-diameter-secant-collinear-tutor-1.jpg) |
Geometry Problem 1404. Three Circles, Center, Intersecting Points, Collinearity, Congruence. |
![Problem 1403](../school-college/5/p1403-quadrilateral-congruence-90-degree-angle-tutor-1.jpg) |
Geometry Problem 1403. Quadrilateral, 90 Degree Angle, Perpendicular, Congruence. |
![Problem 1401](../school-college/5/p1401-rigth-triangle-isosceles-tangent-congruence-tutor-1.jpg) |
Geometry Problem 1401. Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence. |
![Problem 1389 40-120-20 triangle](../school-college/4/p1389-triangle-40-20-degree-angle-congruence-tutoring-1.jpg) |
Geometry Problem 1389. Triangle, 40-120-20 degree, Angle, Congruence. |
![Problem 1388 40-60-80 triangle](../school-college/4/p1388-triangle-40-60-80-degree-incenter-side-congruence-1.jpg) |
Geometry Problem 1388. Triangle 40-60-80 degree, Incenter, Congruence. |
![Problem 1382 Circle, Diameter, Radius, Perpendicular, Congruence](../school-college/4/p1382-circle-diameter-perpendicular-congruence-tutoring-1.jpg) |
Geometry Problem 1382. Circle, Diameter, Radius, Perpendicular, Congruence. |
![Problem 1380 Circles, Tangents, Chords](../school-college/4/p1380-two-circle-common-internal-tangent-congruent-chord-1.jpg) |
Geometry Problem 1380. Common
Internal Tangents. Circles, Secant, Congruent Chords. |
![Problem 1379 Circles, Tangents, Chords](../school-college/4/p1379-two-circle-common-external-tangent-congruent-chord-1.jpg) |
Geometry Problem 1379. Common External Tangents. Circles, Secant, Congruent Chords. |
![Geometry problem 1361](../school-college/4/p1361-two-nine-point-circle-angle-tutor-sketch-sw-1.jpg) |
Geometry Problem 1361.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, 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 1356](../school-college/4/p1356-triangle-30-degrees-angle-congruence-tutoring-1.jpg) |
Geometry Problem 1356.
Quadrilateral, Triangle, Angle, 30 Degrees, Congruence. |
![Geometry problem 1353](../school-college/4/p1353-tangent-circle-congruence-30-degrees-1.jpg) |
Geometry Problem 1353. Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees. |
![Geometry problem 1349](../school-college/4/p1349-three-equal-squares-90-degrees-diagonal-infographic-classes-1.jpg) |
Geometry Problem 1349. Three Squares, 90 Degrees, Perpendicular Lines, Diagonal. Math Infographic. |
![Geometry problem 1348](../school-college/4/p1348-concentric-circles-equilateral-triangle-tutoring-1.jpg) |
Geometry Problem 1348. Three Concentric Circles, Equilateral Triangle, Perpendicular Bisector, Congruence. |
![Geometry problem 1347](../school-college/4/p1347-equilateral-triangle-bisector-circle-tangent-tutoring-1.jpg) |
Geometry Problem 1347. Triangle, Angle Bisector, Congruence, Circumcircle, Tangent, Equilateral Triangle. |
![Geometry problem 1329](../school-college/4/p1329-two-squares-90-degree-parallel-congruence-1.jpg) |
Geometry Problem 1329.
Two Squares Side by Side, Parallel, Perpendicular, 90 Degrees, Congruence. |
![Geometry problem 1328](../school-college/4/p1328-two-squares-90-degree-congruence-1.jpg) |
Geometry Problem 1328.
Two Squares Side by Side, Perpendicular, 90 Degrees, Congruence. |
![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 1315](../school-college/4/p1315-triangle-incircle-tangent-chord-congruence-1.jpg) |
Geometry Problem 1315.
Triangle, Incircle, Tangent, Chord, Circle, Congruence. |
![Geometry problem 1314](../school-college/4/p1314-equilateral-triangle-incircle-tangent-congruence-1.jpg) |
Geometry Problem 1314.
Equilateral Triangle, Incircle, Inscribed Circle, Tangent, Congruence. |
![Geometry problem 1313](../school-college/4/p1313-decagon-pentadecagon-equilateral-triangle-1.jpg) |
Geometry Problem 1313.
Regular Decagon, Pentadecagon, Equilateral Triangle, Congruence. |
![Geometry problem 1304](../school-college/4/p1304-triangle-120-degrees-angle-bisector-1.jpg) |
Geometry Problem 1304.
Triangle, 120 Degrees, Angle Bisector, Measurement. |
![Geometry problem 1303](../school-college/4/p1303-triangle-60-degrees-angle-bisector-1.jpg) |
Geometry Problem 1303.
Triangle, 60 Degrees, Angle Bisector, Measurement. |
![Geometry problem 1302](../school-college/4/p1302-triangle-median-circle-congruence-1.jpg) |
Geometry Problem 1302.
Triangle, Median, Midpoint, Circles, Diameters, Congruence. |
![Geometry problem 1295](../school-college/3/p1295-right-triangle-incenter-excenter-angle-1.jpg) |
Geometry Problem 1295.
Right Triangle, Incenter, Incircle, Excenter, Excircle, Congruence, Angle. |
![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. |
![Geometry problem 1287](../school-college/3/p1287-isosceles-triangle-40-100-40-degrees-1.jpg) |
Geometry Problem 1287.
Triangle, 40-100-40 Degrees, Congruence, Area, Metric Relations, Measurement. |
![Geometry problem 1286](../school-college/3/p1286-quadrilateral-60-135-105-degrees-measurement-1.jpg) |
Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement. |
![Geometry problem 1285](../school-college/3/p1285-quadrilateral-60-150-90-degrees-measurement-1.jpg) |
Geometry Problem 1285.
Triangle, Quadrilateral, 60, 150, 90 Degree Angles, Congruence, Measurement. |
![Geometry problem 1284](../school-college/3/p1284-equilateral-triangle-midpoint-1.jpg) |
Geometry Problem 1284.
Two Equilateral Triangle, Midpoint, Congruence. |
![Geometry problem 1278](../school-college/3/p1278-square-3-4-5-right-triangle-tutoring-1.jpg) |
Geometry Problem 1278.
Square, 3-4-5 Right Triangle, Midpoint. |
![Geometry problem 1272](../school-college/3/p1272-isosceles-triangle-altitude-midpoint-angle-1.jpg) |
Geometry Problem 1272.
Isosceles Triangle, Median, Midpoint, Perpendicular, 90 Degrees, Angles, Congruence. |
![Geometry problem 1250](../school-college/3/p1250-cyclic-quadrilateral-circle-diameter-congruence-1.jpg) |
Geometry Problem 1250.
Cyclic or Inscribed Quadrilateral, Circle, Diameter, Congruence. |
![Geometry problem 1238](../school-college/3/p1238-square-equilateral-triangle-metric-relation-mobile-apps-1.jpg) |
Geometry Problem 1238
Square, Equilateral Triangle, Metric Relations. Mobile Apps. |
![Geometry problem 1237](../school-college/3/p1237-imo-2016-problem-1-triangle-parallel-concurrent-1.jpg) |
Geometry Problem 1237
IMO 2016, Problem 1, Triangle, Congruence, Parallel Lines, Midpoint, Concurrency. |
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