Squares, Theorems and Problems

Online Geometry: Similarity, Ratios, Proportions. Theorems and Problems. Page 2 of 5

Similarity

Problem 839: Parallelogram, Perpendicular, Diagonal, Metric Relations

Geometry Problem 839
Problem 839: Parallelogram, Perpendicular, Diagonal, Metric Relations.

Parallelogram, Perpendicular, Diagonal, Similarity, Metric Relations

Geometry Problem 836
Parallelogram, Perpendicular, Diagonal, Similarity, Metric Relations.

Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional

Geometry Problem 834
Parallelogram, Diagonal, Similarity, Geometric Mean, Mean Proportional.

Parallelogram, Diagonal, Similarity, Proportion

Geometry Problem 833
Parallelogram, Diagonal, Similarity, Proportion.

Triangle, Circumcenter, Similarity

Geometry Problem 806
Triangle, Points on sides, Circumcenter, Similarity.

Parallelogram, Angle Bisector

Geometry Problem 797
Parallelogram, Angle Bisector, Isosceles and Similar Triangles.

Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations

Geometry Problem 772
Similar triangles with a Common Vertex, Equal Angles, Midpoints, Metric relations.

Parallelogram, COngruence, Angle Bisector

Geometry Problem 751.
Parallelogram, Congruence, Intersecting Lines, Angle Bisector.

Complete Quadrilateral, Triangle, Diagonal, Parallel, Similarity

Geometry Problem 750.
Complete Quadrilateral, Triangle, Diagonal, Parallel, Similarity, Metric Relations.

Trapezoid, Parallel, Harmonic Mean

Geometry Problem 747.
Trapezoid, Diagonals, Parallel, Bases, Midpoint, Similarity, Harmonic Mean, Metric Relations.

Triangle, Parallel, Similarity, Harmonic Mean

Geometry Problem 746.
Triangle, Cevian, Parallel, Similarity, Harmonic Mean, Metric Relations.

Parallelogram, Midpoint, Diagonal, Collinear, Metric Relations, Similarity, Congruence

Geometry Problem 710.
Parallelogram, Midpoint, Diagonal, Collinear Points, Metric Relations, Triangle, Similarity, Congruence.

Triangle, Circle, Median, Proportion

Geometry Problem 679.
Triangle, Circle, Median, Proportion.

Parallelogram, Midpoint, Diagonal

Geometry Problem 677.
Parallelogram, Midpoint, Diagonal, Metric Relations.

Triangle, Incenter, Excenter, Distance

Geometry Problem 626
Triangle, Distance from the Incenter to an Excenter.

Triangle, Parallel, Angle Bisector

Geometry Problem 625
Triangle, Parallel Lines, Congruence, Angle Bisector, Similarity.

Quadrilateral, transversal, ratio, similarity

Proposed Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity.

Problem 433: Quadrilateral, Area

Proposed Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Problem 432: Trapezoid, Parallel, Similarity

Proposed Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal.

Quadrilateral, Midpoint diagonals

Proposed Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal.

Inscribed and Circumscribed regular Pentagon, Areas

Proposed Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas, Similarity.

Square, 45 degrees

Proposed Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

Pythagorean Theorem

Proposed Problem 265.
Right Triangle, Pythagorean Theorem, Similarity.

Right triangle

Proposed Problem 264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean.

Mascheroni Construction with compass alone. Midpoint of a segment, Similarity.

Stewart Theorem

Stewart Theorem Triangle, sides and a cevian.

Heron's Formula.
Key facts and
a purely geometric step-by-step proof.
 

Heron's Formula with medians 

Gergonne Point Theorem

Gergonne Point Theorem. Concurrency. Interactive proof with animation.

Key concept: Ceva's Theorem.
 

Ceva's theorem

Ceva's Theorem. Concurrency. Interactive proof with animation. Key concept: Menelaus Theorem.
Similarity.

Nine-Point Center, Nine-Point Circle, Euler Line.
Interactive illustration.

Puzzle of the Ceva's Theorem: 48 classic piece.

Menelaus' Theorem. Interactive proof with animation and key concepts.

Gergonne's theorem

Gergonne's Theorem: Triangle and Concurrent Cevians.

Van Aubel's theorem II

Van Aubel's Theorem II: Triangle and Cevians.
 

Proposed Problem 64: Triangle, Incircle, Transversal.

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