Triangles Theorems and Problems-
Page 9
|
![Triangles](../geometry/triangles_index_17.jpg) |
|
![Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Parallel, Congruence, Similarity](../school-college/p843-triangle-centroid-four-circumcenter-perpendicular-parallel-similarity-1.jpg) |
Geometry Problem 843
Triangle, Medians, Centroid, Four Circumcenters,
Perpendicular, Parallel, Congruence, Similarity. |
![Triangle, Medians, Centroid, Four Circumcenters, Perpendicular, Congruence, Similarity](../school-college/p842-triangle-centroid-four-circumcenter-perpendicular-similarity-1.jpg) |
Geometry Problem 842
Triangle, Medians, Centroid, Four Circumcenters,
Perpendicular, Congruence, Similarity. |
![Triangle, Medians, Centroid, Circumcenters, Perpendicular, Congruence, Similarity](../school-college/p841-triangle-centroid-circumcenter-perpendicular-similarity-1.jpg) |
Geometry Problem 841
Triangle, Medians, Centroid, Circumcenters, Perpendicular, Congruence,
Similarity. |
![Parallelogram, Perpendicular, Diagonal, Metric Relations, Similarity](../school-college/p840-parallelogram-perpenddicular-sides-diagonal-1.jpg) |
Geometry Problem 840
Parallelogram, Perpendicular, Diagonal, Metric Relations, Similarity. |
![Problem 839: Parallelogram, Perpendicular, Diagonal, Metric Relations](../school-college/p839-parallelogram-perpendicular-sides-projection-1.jpg) |
Geometry Problem 839
Problem 839: Parallelogram, Perpendicular, Diagonal, Metric Relations. |
![Parallelogram, Perpendicular, Diagonal, Metric Relations](../school-college/p838-parallelogram-perpendicular-diagonal-metric-relations-1.jpg) |
Geometry Problem 838
Parallelogram, Perpendicular, Diagonal, Metric Relations. |
![Triangle, Orthocenter, Circumcenter, Circle, Concyclic Points](../school-college/p837-triangle-orthocenter-circumcenter-concyclic-1.jpg) |
Geometry Problem 837
Triangle, Orthocenter, Circumcenter, Circle, Concyclic Points. |
![Parallelogram, Perpendicular, Diagonal, Similarity, Metric Relations](../school-college/p836-parallelogram-perpendicular-diagonal-similarity-1.jpg) |
Geometry Problem 836
Parallelogram, Perpendicular, Diagonal, Similarity, Metric Relations. |
![Isosceles Triangle, Double Angle, Triple Angle, Auxiliary Lines](../school-college/p835-isosceles-triangle-angle-double-triple-auxiliary-lines-1.jpg) |
Geometry Problem 835
Isosceles Triangle, Double Angle, Triple Angle, Auxiliary Lines. |
![Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional](../school-college/p834-parallelogram-diagonal-geometric-mean-proportional-1.jpg) |
Geometry Problem 834
Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional. |
![Parallelogram, Diagonal, Similarity, Proportion](../school-college/p833-parallelogram-diagonal-proportion-similarity-1.jpg) |
Geometry Problem 833
Parallelogram, Diagonal, Similarity, Proportion. |
![Quadrilateral, Isosceles triangle, 70-70-40 degrees, Congruence](../school-college/p832-quadrilateral-triangle-70-70-40-angle-20-congruence-1.jpg) |
Geometry Problem 832
Quadrilateral, Isosceles triangle, 70-70-40 degrees, Congruence, Auxiliary lines, Equilateral triangle. |
![Quadrilateral, Triangle, Angles, 30 degrees, Congruence](../school-college/p831-quadrilateral-diagonal-midpoint-parallelogram-1.jpg) |
Geometry Problem 831
Quadrilateral, Diagonal, Midpoint, Opposite Angles, Congruence, Parallelogram. |
![Quadrilateral, Triangle, Angles, 30 degrees, Congruence](../school-college/p830-triangle-quadrilateral-30-degree-congruence-1.jpg) |
Geometry Problem 830
Quadrilateral, Triangle, Angles, 30 degrees, Congruence. |
![Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations](../school-college/p829-triangle-circumcircle-parallel-metric-relation-1.jpg) |
Geometry Problem 829
Triangle, Circumcircle, Parallel, Chord, Side, Metric Relations. |
![Geometry Problem Quadrilateral Midpoint](../school-college/p828-quadrilateral-midpoint-opposite-sides-diagonals-concurrent-1.jpg) |
Geometry Problem 828
Quadrilateral, Midpoint, Opposite sides, Diagonals, Concurrent lines, Triangle, Bimedian. |
![Semicircle, Chord, Arc, Area](../school-college/p825-semicircle-triangle-area-diameter-chord-arc-midpoint-sector-1.jpg) |
Geometry Problem 825.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area. |
![Desargues' Theorem, Triangles in Perspective](../school-college/p824-desargues-theorem-perspective-triangles-1.jpg) |
Geometry Problem 824
Desargues' Theorem, Triangles in Perspective. |
![Tangent Circles, Diameter, Perpendicular, Triangle, Area, Tangency Point](../school-college/p823-circle-triangle-area-perpendicular-tangent-diameter-1.jpg) |
Geometry Problem 823.
Tangent Circles, Diameter, Perpendicular, Chord, Secant, Triangle, Area, Tangency Point. |
![Semicircle, Chord, Arc, Area](../school-college/p822-circle-triangle-area-diameter-chord-midpoint-sector-1.jpg) |
Geometry Problem 822.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area. |
![Adams Circle](../school-college/p821-adams-circle-theorem-1.jpg) |
Geometry Problem 821.
Adams Circle. |
![Triangle, Angles, 30 Degrees](../school-college/p820-triangle-cevian-30-degrees-angle-1.jpg) |
Geometry Problem 820.
Triangle, Cevian, Angles, 30 Degrees. |
![Quadrilateral, Triangle, Angles](../school-college/p819-quadrilateral-triangle-angle-30-degrees-1.jpg) |
Geometry Problem 819.
Quadrilateral, Triangle, Angles, 30 degrees. |
![Square, Triangle, Angle](../school-college/p818-square-triangle-angles-1.jpg) |
Geometry Problem 818.
Square, Triangle, Angle. |
![Triangle, Incircle, Arbelos, Area](../school-college/p815-triangle-incircle-semicircle-tangent-arbelos-area-1.jpg) |
Geometry Problem
815.
Triangle, Incircle, Semicircles, Arbelos, Area. |
![Equilateral triangles, a common vertex](../school-college/p814-two-equilateral-triangle-vertex-angle-1.jpg) |
Geometry Problem
814.
Two Equilateral Triangles with a common Vertex, Angle. |
![Trisecting a line segment, 4 circles](../school-college/p811-trisecting-segment-4-circles-one-line-1.jpg) |
Geometry Problem
811: Trisecting a line segment.
With four circles and one line. |
![Trisecting a line segment, 2 circles](../school-college/p810-trisecting-segment-2-circles-8-lines-1.jpg) |
Geometry Problem
810: Trisecting a line segment.
With two circles and eight lines. |
![Trisecting a segment with three circles](../school-college/p809-trisecting-segment-3-circles-4-lines-1.jpg) |
Geometry Problem
809: Trisecting a line segment.
With three circles and four lines. |
![Parallelogram, Perpendicular, Semicircle, Area](../school-college/p808-parallelogram-perpendicular-right-triangle-semicircle-area-1.jpg) |
Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter. |
![Right Triangle Area, Incircle, Semicircle](../school-college/p807-right-triangle-area-semicircle-incircle-1.jpg) |
Geometry Problem 807
Right Triangle Area, Incircle, Tangency Points, Semicircle Area. |
![Triangle, Circumcenter, Similarity](../school-college/p806-triangle-circumcenter-similarity-1.jpg) |
Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity. |
![Stewart Theorem](../pythagoras/stewart_theorem_170.jpg) |
Geometry Problem 805, Stewart Theorem
Triangle, sides and a cevian.
|
![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. |
|
Geoboard
for iPad Pythagorean Theorem Proof, Squares (Problem 540). |
![Scalene Triangle, Median, Perpendicular, Angle, Measurement](../school-college/p802-triangle-median-perpendicular-angle-1.jpg) |
Geometry Problem
802
Scalene Triangle, Median, Perpendicular, Angle, Measurement. |
![Equilateral Triangles, Midpoint](../school-college/p801-equilateral-triangle-metric-relation-1.jpg) |
Geometry Problem
801
Equilateral Triangles, Cevian, Midpoint, Distance, Measurement, Metric Relations. |
![Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter](../school-college/p799-parallelogram-angle-bisector-circumcircle-circumcenter-1.jpg) |
Geometry Problem 799
Parallelogram, Angle Bisector, Parallel, Triangle, Circumcircle, Circumcenter. |
![Parallelogram, Secant Line, Tangent Circles, Triangle](../school-college/p798-parallelogram-secant-line-tangent-circles-1.jpg) |
Geometry Problem 798
Parallelogram, Secant Line, Tangent Circles, Circumcircles, Triangle. |
![Parallelogram, Angle Bisector](../school-college/p797-parallelogram-angle-bisector-isosceles-1.jpg) |
Geometry Problem 797
Parallelogram, Angle Bisector, Isosceles and Similar Triangles. |
![Triangle, Altitude, Angle](../school-college/p796-triangle-altitude-perpendicular-angle-1.jpg) |
Geometry Problem 796
Triangle, Altitude, Measurement of Angles. |
![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. |
![Regular Hexagon, Midpoints, Equilateral Triangle](../school-college/p791-regular-hexagon-midpoint-equilateral-triangle-area-1.jpg) |
Geometry Problem 791
Regular Hexagon, Midpoints of Side and Diagonal, Equilateral Triangle, Area. |
![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. |
![Equilateral Triangle, Parallel, Perpendicular](../school-college/p785-equilateral-triangle-parallel-perpendicular-1.jpg) |
Geometry Problem 785
Equilateral
Triangle, Parallel, Perpendicular. |
![Triangle, Orthocenter, Midpoint](../school-college/p784-triangle-orthocenter-midpoint-perpendicular-1.jpg) |
Geometry Problem 784
Triangle, Orthocenter, Midpoint of a side, Perpendicular. |
![Triangle, Orthocenter, Circumcircle, Diameter, Midpoint](../school-college/p783-triangle-orthocenter-circumcircle-diameter-midpoint-1.jpg) |
Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Midpoint. |
![Triangle, Orthocenter, Circumcircle, Diameter, Altitude, Parallelogram](../school-college/p782-triangle-orthocenter-circumcircle-diameter-parallelogram-1.jpg) |
Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram. |
![Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular](../school-college/p781-triangle-circumcenter-perpendicular-orthocenter-midpoint-1.jpg) |
Geometry Problem 781
Triangle, Orthocenter, Circumcenter, Vertex, Altitude, Midpoint, Perpendicular. |
![Triangle, Orthocenter, Inradius, Circumradius](../problem/p780-triangle-distance-orthocenter-vertex-circumradius-inradius-1.jpg) |
Geometry Problem 780
Triangle, Sum of Inradius and Circumradius, Distances from the Orthocenter to the Vertices. |
![Triangle, Orthocenter, Midpoint, 90 Degrees](../problem/p779-triangle-altitude-orthocenter-midpoint-90-degrees-1.jpg) |
Geometry Problem 779
Triangle, Altitude, Orthocenter, Midpoint, Angle, 90 Degrees. |
![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. |
![Triangle, Distance from the Orthocenter, Vertex, Circle, Circumradius, Cosine](../problem/p777-triangle-altitude-orthocenter-vertex-circumradius-cosine-1.jpg) |
Geometry Problem 777
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Cosine. |
![Triangle, Isogonal lines, Congruent angles, Perpendicular](../problem/p776-triangle-isogonal-perpendicular-feet-concyclic-midpoint-1.jpg) |
Geometry Problem 776
Triangle, Isogonal lines, Congruent angles, Perpendicular, Concyclic points, Circle, Center, Midpoint. |
![Triangle, Isogonal lines, Congruent angles, Perpendicular](../problem/p775-triangle-isogonal-perpendicular-feet-metric-relation-1.jpg) |
Geometry Problem 775
Triangle, Isogonal lines, Congruent angles, Perpendicular, Metric Relations. |
![Triangle, Two Altitudes, Circumcircle, Tangent, Parallel](../problem/p774-triangle-circumcircle-altitude-tangent-parallel-1.jpg) |
Geometry Problem 774
Triangle, Two Altitudes, Circumcircle, Tangent at a Vertex, Parallel. |
![Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations](../problem/p772-triangles-common-vertex-similarity-sas-midpoint-1.jpg) |
Geometry Problem 772
Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations. |
![Parallelogram, Star, Pentagon, Area](../problem/p771-parallelogram-star-pentagon-triangle-area-1.jpg) |
Geometry Problem 771
Area of a Parallelogram, Star, Pentagon, Triangles. |
![Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint arc, Parallel chord, Congruence](../problem/p770-parallelogram-triangle-circumcenter-angle-bisector-1.jpg) |
Geometry Problem 770
Parallelogram, Angle Bisector, Triangle, Circumcenter, Circumcircle, Angle Measurement. |
![Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint arc, Parallel chord, Congruence](../problem/p769-triangle-circumcenter-orthocenter-midpoint-arc-parallel-congruence-1.jpg) |
Geometry Problem 769
Triangle, Circumcircle, Circumcenter, Orthocenter, Midpoint of arc, Parallel to chord, Congruence. |
![Parallelogram with wquilateral triangles](../problem/p768-parallelograms-equilateral-triangles-1.jpg) |
Geometry Problem 768
Parallelogram with Equilateral Triangles on Sides. |
![Equilateral triangle, Circle, Tangent](../problem/p767-equilateral-triangle-tangent-to-circle-1.jpg) |
Geometry Problem 767
Equilateral Triangle, Circle tangent to a side, Tangent line, Measurement, Secant. |
![Triangle, Inradius, Exradii, Harmonic Mean](../problem/p766-triangle-altitudes-exradii-equal-harmonic-mean-1.jpg) |
Geometry Problem 766
Triangle, Altitudes, Exradii, Three Exradius, Equal Harmonic Mean. |
![Triangle, Inradius, Exradii, Harmonic Mean](../problem/p765-triangle-inradius-exradius-exradii-harmonic-mean-1.jpg) |
Geometry Problem 765
Triangle, Inradius, Exradii, Three Exradius, Harmonic Mean. |
![Triangle, Inradius, Altitudes, Harmonic Mean](../problem/p764-triangle-altitudes-inradius-harmonic-mean-1.jpg) |
Geometry Problem 764
Triangle, Inradius, Altitudes, Harmonic Mean. |
![Parallelogram, Diagonal, Parallel, Congruence](../problem/p763-parallelogram-diagonal-parallel-congruence-1.jpg) |
Geometry Problem 763
Parallelogram, Diagonal, Parallel, Congruence. |
![Parallelogram, Midpoint, Perpendicular, Congruence, Isosceles triangle](../problem/p762-parallelogram-midpoint-perpendicular-congruence-1.jpg) |
Geometry Problem 762
Parallelogram, Midpoint, Perpendicular, Congruence, Isosceles triangle. |
![Scalene Triangle with an angle of 60 degrees, Euler Line, Equilateral Triangle](../problem/p761-triangle-60-degrees-euler-line-equilateral-1.jpg) |
Geometry Problem 761
Scalene Triangle with an angle of 60 degrees, Euler Line, Equilateral Triangle. |
![Isosceles Triangle, Circle, Diameter, Altitude, Chord](../problem/p760-isosceles-triangle-circle-diameter-metric-relations-1.jpg) |
Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations. |
![Equilateral Triangle,Trisection, Cevian, Perpendicular](../problem/p759-equilateral-triangle-transversal-60-degrees-1.jpg) |
Geometry Problem 759
Equilateral Triangle, Transversal, Trisection of sides, Congruence, Angle. |
![Equilateral Triangle,Trisection, Cevian, Perpendicular](../problem/p758-equilateral-triangle-trisection-perpendicular-1.jpg) |
Geometry Problem 758
Equilateral Triangle, Cevians, Trisection of sides, Congruence, Perpendicular, 90 Degrees. |
![Equilateral Triangle, Circumcircle, Chord, Harmonic Mean](../problem/p757-equilateral-triangle-circumcircle-harmonic-mean-1.jpg) |
Geometry Problem 757
Equilateral Triangle, Circumcircle, Chords, a Half of Harmonic Mean. |
![Equilateral triangle, Circumcircle, Midpoint](../problem/p755-equilateral-triangle-circumcircle-midpoint-perpendicular-1.jpg) |
Geometry Problem 755.
Equilateral Triangle, Circumcircle, Chord, Arc, Midpoints, Perpendicular. |
![Equilateral triangle, Perimeter](../problem/p754-equilateral-triangle-60-degrees-center-sum-1.jpg) |
Geometry Problem 754.
Equilateral Triangle, Center, Angle, 60 Degrees, Perimeter. |
![Trisngle, Orthocenter, Ratio](../problem/p753-triangle-altitude-orthocenter-ratio-1.jpg) |
Geometry Problem 753.
Triangle, Altitudes, Orthocenter, Sum of ratios. |
Go to Page: Previous |
1 |
2 |
3
| 4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
40 |
Next
|