![Pythagoras and Right Triangles and Problems](../machu_picchu_h1_810.jpg)
Plane Geometry: Pythagoras, Right Triangle, Metric Relations
- Index 2
Pythagoras' truth,
Right triangle's sacred gift,
Sides in harmony.
Square of hypotenuse sings,
Geometry's masterpiece.
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![](lunes_hippocrates_04_170.jpg) |
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![Geometry Problem 1110](../school-college/2/p1110-right-triangle-square-angle-bisector-math-1.jpg) |
Geometry Problem
1110.
Right Triangle, External Squares, Catheti, Cathetus, Angle Bisector, 45 Degree, Internal Square. |
![Geometry Problem 1109](../school-college/2/p1109-right-triangle-square-45-degree-angle-math-1.jpg) |
Geometry Problem
1109.
Right Triangle, External Squares, Catheti, Cathetus, 45 Degree, Angle. |
![Geometry Problem 1108](../school-college/2/p1108-right-triangle-square-harmonic-mean-congruence-math-1.jpg) |
Geometry Problem
1108.
Right Triangle, External Squares, Catheti, Cathetus, Congruence, Harmonic Mean. |
![Geometry Problem 1104](../school-college/2/p1104-right-triangle-tangent-circle-radius-math-tutor-1.jpg) |
Geometry Problem
1104.
Right Triangle, Incircle, Circumcircle, Inscribed Circle, Radius,
Tangent. |
![Geometry Problem 1103](../school-college/2/p1103-right-triangle-circle-radius-geometric-mean-math-sangaku-1.jpg) |
Geometry Problem
1103.
Right Triangle, Incircle, Inscribed Circle, Radius, Geometric Mean, Sangaku, Japanese, Metric Relations. |
![Geometry Problem 1102](../school-college/2/p1102-right-triangle-circle-perpendicular-incircle-cathetus-math-1.jpg) |
Geometry Problem
1102.
Right Triangle, Incircle, Tangency Point, 90 Degree, Cathetus, Metric Relations. |
![Geometry Problem 1075](../school-college/1/p1075-triangle-90-degrees-quadrilateral-midpoint-distance-geometry-math-1.jpg) |
Geometry Problem
1075.
Quadrilateral, Right Triangle, 90 Degrees, Isosceles, Midpoint, Distance. |
![Geometry Problem 1043](../school-college/1/p1043-right-triangle-incenter-excenter-congruence-math-1.jpg) |
Geometry Problem
1043.
Right Triangle, Incenter, Excenter, Congruence, Metric Relations. |
![Geometry Problem 1018](../school-college/1/p1018-right-triangle-circle-vertices-angle-math-1.jpg) |
Geometry Problem
1018.
Right Triangle, Circles, Angle. |
![Geometry Problem 1015](../school-college/1/p1015-right-triangle-square-altitude-metric-relations-math-1.jpg) |
Geometry Problem
1015.
Right Triangle, Square, Altitude, Metric Relations. |
![Geometry Problem 999](../school-college/p999-right-triangle-double-angle-congruence-math-1.jpg) |
Geometry Problem 999.
Right Triangle, Midpoint, Median, Double Angle, Congruence. |
![Geometry Problem 988](../school-college/p988-right-triangle-cevian-30-degrees-triple-angle-1.jpg) |
Geometry Problem 988.
Right Triangle, Cevians, Angles, 30 Degrees, Triple Angle. |
![Geometry Problem 976](../school-college/p976-isosceles-right-triangle-incenter-45-degrees-hypotenuse-1.jpg) |
Geometry Problem 976.
Isosceles Right Triangle, 45 Degrees, Incenter, Angle Bisector, Hypotenuse. |
![Geometry Problem 975](../school-college/p975-isosceles-right-triangle-angle-bisector-45-degrees-hypotenuse-1.jpg) |
Geometry Problem 975.
Isosceles Right Triangle, 45 Degrees, Angle Bisector, Hypotenuse. |
![Geometry Problem 973](../school-college/p973-square-three-parallel-vertices-metric-relations-1.jpg) |
Geometry Problem 973.
Three Parallel, Square, Vertices, Distance Between Two Parallel Lines, Side, Metric Relations. |
![Geometry Problem 964](../school-college/p964-right-triangle-10-20-30-degrees-angle-cevian-1.jpg) |
Geometry Problem 964.
Right Triangle, Cevians, Angles, 10, 20, 30 Degrees. |
![Problem 912](../school-college/p912-right-triangle-double-triple-angle-perpendicular-1.jpg) |
Geometry Problem 912.
Right Triangle, Double Angle, Triple Angle, Perpendicular Lines.
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![Problem 911](../school-college/p911-right-triangle-double-triple-angle-cyclic-quadrilateral-1.jpg) |
Geometry Problem 911.
Right Triangle, Double Angle, Triple Angle, Concyclic Points, Cyclic Quadrilateral.
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![Stewart Theorem](../pythagoras/stewart_theorem_170.jpg) |
Geometry Problem 805, Stewart Theorem
Triangle, sides and a cevian.
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![Geometry Problem 876](../school-college/p876-equilateral-triangle-perpendicular-equal-area-1.jpg) |
Geometry Problem 876
Equilateral Triangle, any Point, Perpendicular, Right Triangle Area, Sum of Areas. |
![Right Triangle, Altitude, Angle Bisector, Perpendicular, Measurement](../school-college/p803-right-triangle-altitude-angle-bisector-1.jpg) |
Geometry Problem
803
Right Triangle, Altitude, Angle Bisector, Perpendicular, Measurement. |
![Problem 886](../school-college/p886-right-triangle-incenter-bisector-concyclic-geogebra-html5-ipad-1.jpg) |
Geometry Problem 886
Right Triangle, Incenter, Angle Bisector, Perpendicular, 45 Degrees, Concyclic Points, Isosceles Right Triangle. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus). |
![de Gua's theorem](../solid/gua_theorem_170.jpg) |
Geometry Problem
800: de Gua's Theorem
Pythagorean theorem in 3-D, Tetrahedron, Cubic Vertex, Triangular Pyramid, Apex, Height, Right Triangle Area, Base Area, Projected Area. |
![Right Triangle, Altitude, Incircles, CIrcumcircles, COngruence](../school-college/p794-right-triangle-altitude-incircle-2-circumcircles-congruence-1.jpg) |
Geometry Problem 794
Right Triangle, Altitude, Three Incenters, Circumcircles, Incircle, Congruence. |
![Right Triangle, Altitude, Three Incircles, Circumradius](../school-college/p793-right-triangle-altitude-3-incenters-circumradius-distance-1.jpg) |
Geometry Problem 793
Right Triangle, Altitude, Three Incircles, Incenters, Circumcircle, Circumradius, Perpendicular, Distance. |
![Right Triangle, Altitude, Angle Bisector, Three Incircles, Five Concyclic Points, Circles](../school-college/p792-right-triangle-altitude-3-incenters-concyclic-bisector-1.jpg) |
Geometry Problem 792
Right Triangle, Altitude, Angle Bisector, Three Incircles, Five Concyclic Points, Circles. |
![Right Triangle, Altitude, Incenter, Angle Bisector, Inradius](../school-college/p790-right-triangle-altitude-incenter-inradius-congruence-1.jpg) |
Geometry Problem 790
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line, Congruence. |
![Right Triangle, Altitude, Angle Bisector, Inradius](../school-college/p789-right-triangle-altitude-angle-bisector-inradius-1.jpg) |
Geometry Problem 789
Right Triangle, Altitude, Angle Bisector, Incircle, Tangency Point, Inradius, Circles, Tangent Line. |
![Right Triangle, Inradius, 18 Equal Circles, Line Tangent, Legs, Hypotenuse, Ratio, Metric Relations](../school-college/p787-right-triangle-circles-tangent-legs-hypotenuse-inradius-1.jpg) |
Geometry Problem 787
Right Triangle, Inradius, 18 Equal Circles, Line Tangent, Legs, Hypotenuse, Ratio, Metric Relations. |
![Right Triangle, Altitude, Hypotenuse, Cevian, Perpendicular, Ratio](../school-college/p786-right-triangle-altitude-hypotenuse-perpendicular-metric-relations-1.jpg) |
Geometry Problem 786
Right Triangle, Altitude, Hypotenuse, Cevian, Perpendicular, Ratio, Metric relations. |
![Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.](../problem/p778-triangle-altitude-orthocenter-vertex-circumradius-side-1.jpg) |
Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square. |
![Right triangle, Incircles](../problem/p668_right_triangle_1.jpg) |
Geometry Problem 668.
Right triangle, Incircles, Parallel, Common Tangent, Mind Map. |
![Right triangle, Altitude, Incenter, Area](../problem/p634_right_triangle_area_1.jpg) |
Geometry Problem 634
Right Triangle, Altitude, Incenters, Areas. |
![Right triangle area](../problem/p617_triangle_90_area_1.jpg) |
Geometry Problem
617
Right Triangle Area, Incircle, Incenter, Tangent, 90 Degrees. |
![Square with Right triangles](../problem/p608_square_triangle_1.jpg) |
Geometry Problem
608
Square with Right Triangles, Metric Relations, Congruence, Measurement. |
![Online Math: Geometry Problem 572, Right triangle and Circle](../problem/p572_right_triangle_circle1.jpg) |
Problem
572.
Right triangle, Median, Circle, Diameter, Excircle, Tangent circles. |
![Online education: Geometry Problem 570, Collinearity](../problem/p570_square_collinearity_1.jpg) |
Problem
570.
Square, Center, Right Triangles, Congruence, Collinearity. |
![Geometry problem 567](../problem/p567_right_triangle_1.jpg) |
Problem
567.
Right triangle, Incircle, Excircle, Collinear tangency points. |
![Right triangle, Square, Area](../pythagoras/p539_right_triangle_area_1.jpg) |
Problem
539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
![Right triangle, Square, Area](p540_right_triangle_area_1.jpg) |
Problem
540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
![](lunes_hippocrates_01_170.jpg) |
Lunes of
Hippocrates 1
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![](lunes_hippocrates_02_170.jpg) |
Lunes of
Hippocrates 2
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![](lunes_hippocrates_03_170.jpg) |
Lunes of
Hippocrates 3
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![](lunes_hippocrates_04_170.jpg) |
Lunes of
Hippocrates 4
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![Right Triangle, Altitude, Median, Equal angles, Measure](../problem/p544_right_triangle_1.jpg) |
Problem
544.
Right Triangle, Altitude, Median, Equal angles, Measure. |
![Right Triangle, Altitude, Angle Bisector, Median](../problem/p543_right_triangle_1.jpg) |
Problem
543.
Right Triangle, Altitude, Angle Bisector, Median. |
![Right triangle, Altitude, Angle Bisectors, 90 Degrees](../problem/p542_right_triangle_1.jpg) |
Problem
542.
Right Triangle, Altitude, Angle Bisector, Perpendicular, 90 Degrees. |
![Right triangle, Altitude, Angle Bisector](../problem/p541_right_triangle_1.jpg) |
Problem
541.
Right Triangle, Altitude, Angle Bisector, Congruence. |
![Right triangle, square, area](../problem/p534_right_triangle_area_1.jpg) |
Problem
534.
Right Triangle, Squares, Perpendicular, Dissection, Areas. |
![Geometry Problem: Right triangle, Circle, Tangent](../problem/p522_triangle_circle_1.jpg) |
Problem 522.
Right Triangle, Circle, Diameter, Tangent. |
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