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Perpendicular Lines, Theorems
and Problems - Table of Content (2)
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![Perpendicular Lines Index](perpendicular_lines_index_1.jpg) |
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![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 1390](../school-college/4/p1390-triangle-point-perpendicular-sum-square-tutoring-1.jpg) |
Geometry Problem 1390. Triangle, any point, perpendicular, sum of the squares. |
![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. |
![Problem 1388 Circle, Triangle](../school-college/4/p1384-triangle-circumcircle-orthocenter-bisector-90-degree-1.jpg) |
Geometry Problem 1384. Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, 90 Degree. |
![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 1378 Parallelogram](../school-college/4/p1378-parallelogram-diagonal-perpendicular-distance-1.jpg) |
Geometry Problem 1378. Parallelogram, Diagonal perpendicular to a side, Distances from a Point to Vertices, Measurement. |
![Geometry problem 1366](../school-college/4/p1366-square-perpendicular-angle-bisector-concylic-1.jpg) |
Geometry Problem 1366.
Square, Angle Bisector, Perpendicular, Concyclic Points, Circle, Sketch, iPad Apps. |
![Geometry problem 1364](../school-college/4/p1364-square-inscribed-circle-chord-pieces-area-1.jpg) |
Geometry Problem 1364.
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps. |
![Geometry problem 1363](../school-college/4/p1363-square-perpendicular-angle-bisector-45-degree-1.jpg) |
Geometry Problem 1363.
Square, Angle Bisector, Perpendicular, 45 Degrees, Angle, Sketch, iPad Apps. |
![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 1351](../school-college/4/p1351-circumscribed-tangential-quadrilateral-midpoint-perpendicular-1.jpg) |
Geometry Problem 1351. Two Tangential or Circumscribed Quadrilaterals, Midpoints, Perpendiculars. |
![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 1346](../school-college/4/p1346-equilateral-triangle-incircle-altitude-tutoring-1.jpg) |
Geometry Problem 1346. Equilateral Triangle, Point on the Incircle, Altitude, Perpendicular, Sum of Squares, Distance. |
![Geometry problem 1343](../school-college/4/p1343-triangle-excircle-tangent-90-degree-1.jpg) |
Problem 1343.
Triangle, Excircles, Circle, Tangent, Tangency Points, Chord, Perpendicular, 90 Degrees, Collinearity. Machu Picchu in the background.
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![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.
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![Geometry problem 1333](../school-college/4/p1333-two-squares-three-triangles-area-1.jpg) |
Geometry Problem 1333.
Two Squares Side by Side, Three Triangles, Area, Measurement. |
![Geometry problem 1332](../school-college/4/p1332-two-squares-side-by-side-triangle-area-1.jpg) |
Geometry Problem 1332.
Two Squares Side by Side, Triangle, Area. |
![Geometry problem 1331](../school-college/4/p1331-two-squares-90-degree-parallel-measurement-1.jpg) |
Geometry Problem 1331.
Two Squares Side by Side, Parallel, Perpendicular, 90 Degrees, Measurement. |
![Geometry problem 1330](../school-college/4/p1330-two-squares-90-45-degree-parallel-1.jpg) |
Geometry Problem 1330.
Two Squares Side by Side, Parallel, 45, 90 Degrees. |
![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 1327](../school-college/4/p1327-two-squares-90-degree-side-by-side-1.jpg) |
Geometry Problem 1327.
Two Squares Side by Side, Perpendicular, 90 Degrees, Angle. |
![Geometry problem 1318](../school-college/4/p1318-equilateral-triangle-rectangle-common-vertex-distances-1.jpg) |
Geometry Problem 1318.
Rectangle, Equilateral Triangle, Distances, Perpendicular, Measurement. |
![Geometry problem 1312](../school-college/4/p1312-triangle-60-degrees-circumcenter-orthocenter-measurement-1.jpg) |
Geometry Problem 1312.
Triangle, 60 Degrees, Circle, Circumcenter, Orthocenter, Altitude, Distance, Perpendicular, Measurement. |
![Geometry problem 1305](../school-college/4/p1305-triangle-angle-bisector-circumcircle-perpendicular-area-1.jpg) |
Geometry Problem 1305.
Triangle, Circumcircle, Angle Bisector, Arc, Perpendicular, Area. |
![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 1300](../school-college/3/p1300-arbelos-incircle-tangent-bisector-concurrency-1.jpg) |
Geometry Problem 1300.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Perpendicular, Concurrent Lines. |
![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 1292](../school-college/3/p1292-square-right-triangle-circle-radius-1.jpg) |
Geometry Problem 1292.
Square, Circle, Right Triangle, Arc, Inradius, Radius, Incircle, 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 1283](../school-college/3/p1283-equilateral-triangle-midpoint-perperpendicular-1.jpg) |
Geometry Problem 1283.
Two Equilateral Triangle, Perpendicular, Midpoint. |
![Geometry problem 1282](../school-college/3/p1282-square-midpoint-perpendicular-tutoring-1.jpg) |
Geometry Problem 1282.
Three Squares, Common Vertex, Midpoint, Perpendicular, 90 Degrees. |
![Geometry problem 1280](../school-college/3/p1280-quadrilateral-perpendicular-diagonal-collinear-tutoring-1.jpg) |
Geometry Problem 1280.
Quadrilateral, Perpendicular Diagonals, Isosceles Right Triangles, 45 Degrees, Collinear Points. |
![Geometry problem 1275](../school-college/3/p1275-equilateral-triangle-projection-measure-1.jpg) |
Geometry Problem 1275.
Equilateral Triangle, Perpendicular, Projection, Metric Relations, Measurement. |
![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 1270](../school-college/3/p1270-triangle-excircle-bisector-90-degree-1.jpg) |
Geometry Problem 1270.
Triangle, Excircle, Excenter, Escribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1269](../school-college/3/p1269-triangle-incircle-bisector-90-degree-1.jpg) |
Geometry Problem 1269.
Triangle, Incircle, Incenter, Inscribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1267](../school-college/3/p1267-triangle-incircle-excircle-90-degree-parallelogram-1.jpg) |
Geometry Problem 1267.
Triangle, Incircle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Parallelogram. |
![Geometry problem 1266](../school-college/3/p1266-triangle-excircle-90-degree-bisector-1.jpg) |
Geometry Problem 1266.
Triangle, Excircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1265](../school-college/3/p1265-triangle-incircle-90-degree-bisector-1.jpg) |
Geometry Problem 1265.
Triangle, Incircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector. |
![Geometry problem 1264](../school-college/3/p1264-triangle-exterior-angle-bisector-90-degree-concurrent
-1.jpg) |
Geometry Problem 1264.
Triangle, Exterior Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1263](../school-college/3/p1263-triangle-medians-90-degree-perpendicular-1.jpg) |
Geometry Problem 1263.
Triangle, Medians, 90 Degrees, Perpendicular. |
![Geometry problem 1262](../school-college/3/p1262-isosceles-triangle-altitude-median-90-degree-1.jpg) |
Geometry Problem 1262.
Isosceles Triangle, Altitude, Medians, 90 Degrees, Perpendicular. |
![Geometry problem 1261](../school-college/3/p1261-cyclic-quadrilateral-angles-3-4-5-1.jpg) |
Geometry Problem 1261.
Cyclic Quadrilateral, Circle, Diameter, Midpoint, Measurement. |
![Geometry problem 1260](../school-college/3/p1260-triangle-angle-bisector-90-degree-concurrent-1.jpg) |
Geometry Problem 1260.
Triangle, Internal Angle Bisector, Circumcircle, Circle, Perpendicular, 90 Degrees, Concurrent Lines. |
![Geometry problem 1257](../school-college/3/p1257-triangle-altitude-90-degree-measurement-1.jpg) |
Geometry Problem 1257.
Triangle, Altitude, Perpendicular, 90 Degree, Measurement. |
![Geometry problem 1253](../school-college/3/p1253-triangle-orthocenter-90-degree-circles-1.jpg) |
Geometry Problem 1253.
Triangle, Orthocenter, Circle, Circumcircle, Altitude, Perpendicular, 90 Degree, Concurrency. |
![Geometry problem 1252](../school-college/3/p1252-hexagon-triangle-area-orthocenter-circumcircle-mind-map-1.jpg) |
Geometry Problem 1252.
Triangle, Circle, Circumcircle, Altitude, Area, Hexagon, Perpendicular, 90 Degrees. Mind Map. |
![Geometry problem 1251](../school-college/3/p1251-triangle-circle-diameter-90-degrees-1.jpg) |
Geometry Problem 1251.
Triangle, Circle, Diameter, Perpendicular, 90 Degrees. |
![Geometry problem 1248](../school-college/3/p1248-triangle-circle-orthocenter-diameter-parallel-1.jpg) |
Geometry Problem 1248.
Triangle, Circumcircle, Circle, Diameter, Orthocenter, Altitude, Parallel Lines. |
![Geometry problem 1247](../school-college/3/p1247-triangle-circumcircle-perpendicular-orthocenter-1.jpg) |
Geometry Problem 1247.
Triangle, Circumcircle, Orthocenter, Altitude, Perpendicular, Midpoint. |
![Geometry problem 1246](../school-college/3/p1246-orthocenter-midpoint-perpendicular-1.jpg) |
Geometry Problem 1246.
Triangle, Orthocenter, Altitude, Midpoint, Perpendicular. |
![Geometry problem 1244](../school-college/3/p1244-circle-perpendicular-secant-measurement-1.jpg) |
Geometry Problem 1244.
Circle, Radius, Perpendicular, Chord, Secant, Measurement. Mobile Apps. |
![Geometry problem 1240](../school-college/3/p1240-triangle-circle-diameter-perpendicular-1.jpg) |
Geometry Problem 1240
Triangle, Circle, Diameter, Circumcircle, Circumcenter, Perpendicular. Mobile Apps. |
![Geometry problem 1233](../school-college/3/p1233-orthic-axis-triangle-euler-line-perpendicular-1.jpg) |
Geometry Problem 1233
Triangle, Euler Line, Orthic Axis, Perpendicular, 90 Degrees, Orthic Triangle. |
![Geometry problem 1232](../school-college/3/p1232-orthic-axis-triangle-altitude-collinear-1.jpg) |
Geometry Problem 1232
Triangle, Altitudes, Orthic Triangle, Collinearity, Orthic Axis. |
![Geometry problem 1229](../school-college/3/p1229-three-tangent-circles-line-3-4-5-triangle-1.jpg) |
Geometry Problem 1229
Three Tangent Circles, Midpoint, Common Tangent Line, 3-4-5 Right Triangle. |
![Geometry problem 1228](../school-college/3/p1228-three-tangent-circles-line-square-1.jpg) |
Geometry Problem 1228
Three Tangent Circles, Midpoint, Major Arc, Common Tangent Line, Square. |
![Geometry problem 1222](../school-college/3/p1222-doubling-the-cube-triangle-90-120-degrees-class-1.jpg) |
Geometry Problem 1222
Doubling the Cube, Triangle, 90, 120 degrees, Perpendicular, Congruence. |
![Geometry problem 1216](../school-college/3/p1216-3-circles-90-degrees-tangent-collinearity-class-1.jpg) |
Geometry Problem 1216
Circle, 90 Degrees, Tangent, Common Chord, Collinearity. |
![Geometry problem 1211](../school-college/3/p1211-right-triangle-altitude-bisector-45-degrees-class-1.jpg) |
Geometry Problem 1211
Right Triangle, Altitude, Angle Bisector, 45 Degrees. |
![Geometry problem 1208](../school-college/3/p1208-triangle-excenter-diameter-perpendicular-area-1.jpg) |
Geometry Problem 1208
Triangle, Circle, Excircle, Excenter, Diameter, Perpendicular, 90 Degrees, Equal Areas. |
![Geometry problem 1203](../school-college/3/p1203-right-triangle-angle-bisector-quadrilateral-congruence-1.jpg) |
Geometry Problem 1203
Right Triangle, Square, Angle Bisector, Three Congruent Quadrilaterals. |
![Geometry problem 1201](../school-college/3/p1201-triangle-interior-perpendicular-bisector-side-area-1.jpg) |
Geometry Problem 1201
Triangle, Interior Perpendicular Bisector, Midpoint, Area. |
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