Free Geometry Problems and Questions writh Solutions
Free geometry tutorials on topics such as reflection, perpendicular bisector, central and inscribed angles, circumcircles, sine law and triangle properties to solve triangle problems. Also geometry problems with detailed solutions on triangles, polygons, parallelograms, trapezoids, pyramids and cones are included. Polar coordinates equations, conversion and graphing are also included. More challenging geometry problems are also included.
- Triangle Problems. Triangle problems with detailed solutions.
- Congruent Triangles Examples and Problems with Solutions.
- Similar Triangles Examples and Problems with Solutions. Definition and theorems on similar triangles including examples and problems with detailed solutions.
- Equilateral Triangles Problems with Solutions.
- Isosceles Triangles Problems with Solutions.
- Area and Perimeter of Right Triangles Problems With Solution.
- Cosine Law Problems. The cosine law is used to solve word problems.
- Sine Law Problems. The sine law is used to solve word problems.
- Triangle Inscribed in a Circle - Problem With Solution. Inscribed right triangle problem with detailed solution.
- Circle Tangent to Right Triangle - Problem With Solution. Solve a right triangle whose sides are all tangent to a circle. Both the problem and its detailed solution are presented.
- Overlapping Circles Problem. Find overlapping area of two circles: problem with detailed solutions.
- Sectors and Circles Problems. Problems, with detailed solutions, related to sectors and circle.
- Two Squares and a Circle - Problem With Solution. A problem, with detailed solution, on a circle inscribed in one square and circumscribed to another, is presented.
- Two Circles and a Square - Problem With Solution. A problem, with detailed solution, on a square inscribed in one circle and circumscribed to another is presented.
- Rectangle Problems. Rectangle problems on area, dimensions, perimeter and diagonal with detailed solutions.
- Geometry Problems on Squares. Square problems on area, diagonal and perimeter, with detailed solutions.
- Parallelogram Problems. Word problems related to parallelograms are presented along with detailed solutions.
- Trapezoid Problems. Trapezoid problems are presented along with detailed solutions.
- Solve a Trapezoid Given its Bases and Legs.
- Rhombus Problems. Rhombus definition and properties are presented along with problems with detailed solutions.
- Polygons Problems. Problems related to regular polygons.
- Area Of Octagon - Problem With Solution. Find the length of one side, the perimeter and area of a regular octagon given the distance between two opposite sides (span).
- Parallel Lines and Angles Problems. Problems related to parallel lines and alternate and corresponding angles.
- 3D Shapes Volume Problems. 3D shapes, such as prisms, volume problems with detailed solutions.
- Compare Volumes of 3D shapes. A problem to compare the volumes of a cone, a cylinder and a hemisphere.
- How to construct a frustum?. If you cut off the top part of a cone with a plane perpendicular to the height of the cone, you obtain a conical frustum. How to construct a frustum given the radius of the base, the radius of the top and the height?
- Cone Problems. Problems related to the surface area and volume of a cone with detailed solutions are presented.
- Pyramid Problems. Pyramid problems related to surface area and volume with detailed solutions.
Other Geometry Problems
- Intercept Theorem and Problems with Solutions.
- Parts of a Circle.
- Tangents to a Circle with Questions and Solutions .
- Intersecting Secant and Tangent Theorem Questions with Solutions .
- Inscribed and Central Angles in Circles. Definitions and theorems related to inscribed and central angles in circles are discussed using examples and problems.
- Intersecting Chords Theorem Questions with Solutions.
- Intersecting Secant Theorem Questions with Solutions.
- Semicircle Thales Theorem with questions and solutions
- Central and Inscribed Angles - Interactive applet. The properties of central and inscribed angles intercepting a common arc in a circle are explored using an interactive geometry applet.
- Triangles. Definitions and properties of triangles in geometry.
- Area of Triangles Problems with Solutions. Use different formulas of the area of a triangle to calculate the areas of triangles and shapes.
- Properties of Triangles. An applet is used to explore,interactively, the properties of triangles.
- Simple Proofs of Pythagorean Theorem and Problems with Solutions.
- Sine law - ambiguous case - applet. The ambiguous case of the sine law, in solving triangle problems, is explored interactively using an applet.
- Altitudes, Medians and Angle Bisectors of a Triangle.
- Triangles, Bisectors and Circumcircles - interactive applet. The properties of perpendicular bisectors in triangles and circumcircles are explored interactively using a geometry Java applet.
- Quadrilaterals, properties and formulas.
- Kite Questions with Solutions.
- Angles in Geometry. Definitions and properties of angles in geometry.
- Parallel Lines and Angles. This tutorial is about the corresponding, interior and exterior angles formed when a transversal line intersects two parallel lines.
- Regular Polygons. Tutorial to develop useful formulas for area of regular polygons.
- Rotation Symmetry in Regular Polygons. An interactive tutorial to explore rotation symmetry of regular polygons and derive a formula for the angle of rotation.
Other Geometry Topics
- Rotation Symmetry of Geometric Shapes. An interactive tutorial to explore rotation symmetry of geometric shapes.
- Perpendicular Bisector Problems with Solutions.
- Table of Formulas for Geometry. A table of formulas for geometry, related to area and perimeter of triangles, rectangles, circles, sectors, and volume of sphere, cone, cylinder are presented.
Challenge Geometry Problems
Geometric Calculators and Worksheets