# 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.

## Geometry Problems

- 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.
- Polygons Problems. Problems related to regular polygons.
- Parallel Lines and Angles Problems. Problems related to parallel lines and alternate and corresponding angles.
- 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.
- 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 Problems. Triangle problems with detailed solutions.
- Equilateral Triangles Problems with Solutions.
- Isosceles Triangles Problems with Solutions.
- 3D Shapes Volume Problems. 3D shapes, such as prisms, volume problems with detailed solutions.
- 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).
- Area and Perimeter of Right Triangles Problems With Solution.
- 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.
- Triangle Inscribed in a Circle - Problem With Solution. Inscribed right triangle problem with detailed solution.
- Similar Triangles Examples and Problems with Solutions. Definition and theorems on similar triangles including examples and problems with detailed solutions.
- 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.
- Congruent Triangles Examples and Problems with 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?
- Parallelogram Problems. Word problems related to parallelograms are presented along with detailed solutions.
- 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.
- 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.

## Challenge Geometry Problems

- Two Tangent Circles and a Square - Problem With Solution. You are given the perimeter of a small circle to find the radius of a larger circle inscribed within a square.
- Kite Within a Square - Problem With Solution. A problem on finding the sine of the angle of a kite within a square.
- Solve Triangle Given Its Perimeter, Altitute and Angle - Problem With Solution.
- Solve Right Triangle Given Perimeter and Altitude - Problem With Solution.
- Triangle and Tangent Circle - Problem With Solution. A problem, on a triangle tangent at two points to a circle, is presented along with detailed solution.
- Three Tangent Circles - Problem With Solution. A problem, on three tangent circles, is presented along with solution.
- Equilateral Triangle Within a Square - Problem With Solution. A problem on the proof of an equilateral triangle within a square is presented along with detailed solution.
- Square Inscribed in Right Triangle - Problem With Solution. Find the side of a square inscribed in a right triangle given the sides of the triangle.

## Geometry Tutorials

- Simple Proofs of Pythagorean Theorem and Problems with Solutions.
- Triangles. Definitions and properties of triangles in geometry.
- Inscribed and Central Angles in Circles. Definitions and theorems related to inscribed and central angles in circles are discussed using examples and problems.
- Area of Triangles Problems with Solutions. Use different formulas of the area of a triangle to calculate the areas of triangles and shapes.
- Parallel Lines and Angles. This tutorial is about the corresponding, interior and exterior angles formed when a transversal line intersects two parallel lines.
- Properties of Triangles. An applet is used to explore,interactively, the properties of triangles.
- Thales' theorem. An applet is used to verify Thales' theorem: An angle inscribed in a semicircle is a right angle.
- 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.
- Rotation Symmetry of Geometric Shapes. An interactive tutorial to explore rotation symmetry of geometric shapes.
- Angles in Geometry. Definitions and properties of angles in geometry.
- 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.
- 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.
- Perpendicular Bisector- Interactive applet. The definition and properties of the perpendicular bisector are explored using a geometry applet.
- Triangles, Bisectors and Circumcircles - interactive applet. The properties of perpendicular bisectors in triangles and circumcircles are explored interactively using a geometry Java applet.
- 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.

## Polar Coordinates

- Plot Points in Polar Coordinates. An interactive tutorial on how to plot points given by their polar coordinates.
- Graphing Polar Equations. This is tutorial on graphing polar equations by hand, or sketching, to help you gain deep understanding of these equations. Several examples with detailed solutions are presented.
- Convert Polar to Rectangular Coordinates and Vice Versa. Problems, with detailed solutions, where polar coordinates are converted into rectangular coordinates and vice versa are presented.
- Convert Equation from Rectangular to Polar Form. Problems were equations in rectangular form are converted to polar form, using the relationship between polar and rectangular coordinates, are presented along with detailed solutions.
- Convert Equation from Polar to Rectangular Form. Equations in polar form are converted into rectangular form, using the relationship between polar and rectangular coordinates. Problems with detailed solutions are presented.

## Geometric Transformations

- Reflection Across a Line. The properties of reflection of shapes across a line are explored using a geometry applet.
- Rotation of Geometric Shapes. The rotations of 2-D shapes are explored.

## Geometric Calculators and Worksheets

- Online Geometry Calculators and Solvers: Several calculators to help in the calculations and solutions of geometry problems.
- Free Geometry Worksheets to Download

Home Page