Geometry Drills: Problems, Answers, and Explanations
Every math concept needs to be practiced for a student to become proficient. Geometry is no exception. Drills may be found in textbooks and online  both interactive and printable. Teachers may also make up their own drills. Some examples of geometry problems are presented here.
Practicing Geometry through Drills
Geometry
Basic geometry may be defined as dealing with the characteristics and connections of lines and points, surfaces and solids, as well as other spatial relationships. Geometry has a number of subsections. The subsections below (not allinclusive) contain sample problems, answers and explanations.
Plane Geometry
Plane geometry includes lines, planes and polygons. Conceptually, lines and planes do not have ends or edges and extend indefinitely, even though we draw points, lines and planes that look like they have size limitations.
 Problem
 True or False?  One way to form two lines is to intersect two planes.
 Answer and Explanation
 False. Planes are flat surfaces that extend indefinitely in all directions, so if they intersect, only one line is formed at the place of intersection.
Solid Geometry
Solid geometry deals with 3dimensional figures. These include prisms, spheres, pyramids, cones and cylinders. Because all of their sides are flat, these shapes may be grouped together in the category of polyhedrons, which also includes other shapes that have more sides (e.g., tetrahedron and octahedron).
 Problem
 You have a cone and a cylinder. The radius of each is five inches, and their height is also equal at 11 inches. What is the ratio of their volumes?
 Answer and Explanation
 The ratio of the cylinder's volume to the cone's volume is 3:1. Use the formulas for the volumes of a cone and a cylinder.
The volume of a cylinder is (pi)(radius squared)(height). Plug in the numbers so the problem looks like this: V = (3.14)(5^2)(11) = 863.5 cubic inches.
The volume of a cone is (1/3)(pi)(radius squared)(height). Use the information from the problem to solve: V = (1/3)(3.14)(5^2)(11) = 287.8 cubic inches.
As a result, the ratio is 863.5 cubic inches to 287.8 cubic inches, which can be reduced to 3:1.
Loci
A locus is a group of points (or lines) that are decided by or satisfy defined conditions. You solve a locus problem by drawing a diagram.
 Problem
 A private detective is searching for the spot where he believes his client's stolen jewels may have been buried. He has information about a rock that is 20 feet from a particular pine tree and ten feet from a certain oak tree. He has deduced that the jewels are the same distance from the rock and the oak tree, and that they are also eight feet from the oak tree. How many possible places will the detective have to look to find the jewels?
 Answer and Explanation
 He will have to look in two places. Draw a diagram with the rock, pine tree and oak tree. The rock and the pine tree must be 20 feet from one another. The oak tree may be placed anywhere that is ten feet from the rock in your drawing, although the detective has an exact location for it.
 Around the oak tree, draw a circle with a radius of eight feet. Draw a straight line between the rock and the pine tree. Bisect it with a perpendicular line. The line will cross the circumference of the circle in two places. If the detective's deductions are accurate, the jewels will be in one of the two places.
Proofs
Giving geometric proofs is basically an exercise in logic. Proofs use predefined theorems to prove solutions to problems. The problem below is only a small representation of the many geometric proofs.
 Problem
 True or False?  A triangle can have sides measuring nine, 11 and 18.
 Answer and Explanation
 True. The pertinent theorem states that if you add any two sides of a triangle, the sum must be larger than the third side. In this case, 9 + 11 = 20, which is greater than 18. Similarly, 11 + 18 = 29, which is greater than nine. Finally, 9 + 18 = 27, which is greater than 11. Since each of the sums of two sides is greater than the third side, nine, 11 and 18 can be the lengths of the sides of a triangle.
Transformations
Transformational geometry is used to understand congruence and similarity by moving a shape, while keeping the same size and proportions. Movements made include flips (or reflections), slides (or glides or translations) and rotations (or turns). A flip is a mirror image; a slide is what it sounds like  sliding the shape to a different place on the plane. A rotation is the figure turned to a different angle. Problems and their solutions are given in terms of coordinates.
 Problem
 True or False?  Using the translation (2, 3), the point (5, 4) will become (3, 1).
 Answer and Explanation
 True. The translation tells you to add two to the xvalue (5) and subtract three from the yvalue (4).
Other Articles You May Be Interested In

One plus one will always equal two...but just how students are taught math is going to change. Nearly every state in the country has adopted the Common Core Standards; for math, this means new and more indepth approaches to teaching the subject. Have we seen the last of traditional algebra and geometry classes?

One of the most useful and widely used rules in mathematics is the Pythagorean theorem. Your child's mastery of this theorem is critical to success in geometry. One helpful method for understanding and remembering a rule like the Pythagorean theorem is to fully explore its meaning and history.
We Found 7 Tutors You Might Be Interested In
Huntington Learning
 What Huntington Learning offers:
 Online and incenter tutoring
 One on one tutoring
 Every Huntington tutor is certified and trained extensively on the most effective teaching methods
K12
 What K12 offers:
 Online tutoring
 Has a strong and effective partnership with public and private schools
 AdvancEDaccredited corporation meeting the highest standards of educational management
Kaplan Kids
 What Kaplan Kids offers:
 Online tutoring
 Customized learning plans
 RealTime Progress Reports track your child's progress
Kumon
 What Kumon offers:
 Incenter tutoring
 Individualized programs for your child
 Helps your child develop the skills and study habits needed to improve their academic performance
Sylvan Learning
 What Sylvan Learning offers:
 Online and incenter tutoring
 Sylvan tutors are certified teachers who provide personalized instruction
 Regular assessment and progress reports
Tutor Doctor
 What Tutor Doctor offers:
 InHome tutoring
 One on one attention by the tutor
 Develops personlized programs by working with your child's existing homework
TutorVista
 What TutorVista offers:
 Online tutoring
 Student works oneonone with a professional tutor
 Using the virtual whiteboard workspace to share problems, solutions and explanations