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

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

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

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

Geometry Problem 833
Parallelogram, Diagonal, Similarity, Proportion.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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. Concurrency. Interactive proof with animation.

Key concept: 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: Triangle and Concurrent Cevians.

Van Aubel's Theorem II: Triangle and Cevians.
 

Proposed Problem 64: Triangle, Incircle, Transversal.