practice and problem solving geometry

Strengthen your foundations in geometry with angles, triangles, and polygons.

Triangles and Hexagons

Get started by thinking about patterns that combine triangles and hexagons.

Strategic Geometry

Work out strategies to solve these area challenges.

Driving on a Polygon

Derive a fundamental theorem of geometry!

End of Unit 1

Complete all lessons above to reach this milestone.

0 of 3 lessons complete

Angle Hunting Axioms

Practice finding missing angles.

Advanced Mental Shortcuts

Learn sneaky strategies for solving tough angle problems.

Internal Angles in a Polygon

Solve angle problems involving polygons that have many sides.

Invariant Angle Sets

Investigate scenarios where the sum of several angles stays constant.

Advanced Angle Hunts

Tackle this last set of angle challenges by combining all of the techniques you've learned so far.

End of Unit 2

0 of 5 lessons complete

• The Triangle Inequality

In what circumstances can you make a triangle?

Congruent and Similar Triangles

When are triangles the same?

Bass Fishing

Investigate a special case where a triangle can be drawn two ways.

• Curry's Paradox

Uh... Where did the missing square go?

End of Unit 3

0 of 4 lessons complete

Composite Figure Warm-ups

Warm up your problem-solving muscles by mixing and matching bits of different shapes.

Adding Lines and Grids

Add lines to help clarify your thinking.

• Complementary Areas

Sometimes it's easier to find the area of what's left after your shape is removed...

Inclusion and Exclusion

What happens when shapes overlap?

• Invariant Areas

When bend, stretch, move and spin parts of these figures, the areas change shape but don't change size.

End of Unit 4

Angles of Regular Polygons

When all of the sides are the same length and all of the angles are the same measure, what else must be true?

Is It Regular?

Can you be absolutely certain that each of these polygons is regular?

Polygon Areas and Lengths

Apply the Pythagorean Theorem to find length and area measures of regular polygons.

Matchstick Polygons

Play around with these polygons made out of matchsticks, q-tips, and toothpicks.

• Stellations

By extending all of the edges of a polygon you can make beautiful stars.

Dissections

Practice your skills polygon problem-solving with these dissected polygon puzzles.

End of Unit 5

0 of 6 lessons complete

Geometric Stumpers

Challenge yourself and use any strategies you want to solve these problems!

Challenging Composites

Extend your best strategies even further and look for shortcuts.

Coordinate Geometry

Return to the coordinate plane for some especially challenging coordinate puzzles.

Advanced Angle Hunting

Go far beyond the first axioms and explore a realm where wild geometry flourishes.

Applying the Pythagorean Theorem

Apply your mastery of triangles to this final exploration!

End of Unit 6

Course description.

In this course, you'll solve delightful geometry puzzles and build a solid foundation of skills for problem-solving with angles, triangles, and polygons. You'll also improve your visual intuition and learn how to come up with clever, creative solutions to tough challenges. This course is the perfect place to start (or continue) your exploration of geometry if you know how to measure angles and calculate the areas of rectangles, circles, and triangles; and want to learn the next level of geometric problem-solving techniques. Additionally, this is a great course to take if you want to strengthen your geometric intuition in preparation for taking a geometry or design course in school. You'll also need to use a little bit of fundamentals-level algebra in this course, but nothing more advanced than two-variable equations, squares, and square roots.

Topics covered

• Angle Axioms
• Angle Hunting Shortcuts
• Composite Area
• Polygon Angles
• Regular Polygons
• Triangle Congruence
• Triangle Similarity

Prerequisites

• Geometry II
• Beautiful Geometry

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Geometry Math Problems - Perimeters

In these lessons, we will learn to solve geometry math problems that involve perimeter.

Related Pages Geometry math problems involving area Area Formula Geometry math problems involving angles More Algebra Word Problems

Geometry word problems involves geometric figures and angles described in words. You would need to be familiar with the formulas in geometry.

Making a sketch of the geometric figure is often helpful.

Geometry Word Problems Involving Perimeter

Example: A triangle has a perimeter of 50. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?

Solution: Step 1: Assign variables:

Let x = length of the equal sides Sketch the figure

Step 2: Write out the formula for perimeter of triangle .

P = sum of the three sides

Step 3: Plug in the values from the question and from the sketch.

50 = x + x + x+ 5

Combine like terms 50 = 3x + 5

Isolate variable x 3x = 50 – 5 3x = 45 x = 15

Be careful! The question requires the length of the third side.

The length of third side = 15 + 5 = 20

Answer: The length of third side is 20.

Geometry Math Problem involving the perimeter of a rectangle

The following two videos give the perimeter of a rectangle, a relationship between the length and width of the rectangle, and use that information to find the exact value of the length and width.

Example: A rectangular garden is 2.5 times as long as it is wide. It has a perimeter of 168 ft. How long and wide is the garden?

Example: A rectangular landing strip for an airplane has perimeter 8000 ft. If the length is 10 ft longer than 35 times the width, what is the length and width?

Examples of perimeter geometry word problems This video shows how to write an equation and find the dimensions of a rectangle knowing the perimeter and some information about the about the length and width.

Example: The width of a rectangle is 3 ft less than its length. The perimeter of the rectangle is 110 ft. Find the dimensions.

Perimeter Word Problems

Example: The length of a rectangle is 7 cm more than 4 times its width. Its perimeter is 124 cm. Find its dimensions.

Geometry Math Problem involving the perimeter of a triangle

The following two videos give the perimeter of a triangle, a relationship between the sides of the triangle, and use that information to find the exact value or values of the required side or sides.

Example: Patrick’s bike ride follows a triangular path; two legs are equal, the third is 8 miles longer than the other legs. If Patrick rides 30 miles total, what is the length of the longest leg?

Example: The perimeter of a triangle is 56 cm. The first side is 6 cm shorter than the second side. The third side is 2 cm shorter than twice the length of the first side. What is the length of each side?

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HIGH SCHOOL MATH COMMON-CORE GEOMETRY PRACTICE/PROBLEM SOLVING WORKBOOK GRADE 9/10 Paperback – January 1, 2011

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• Language English
• Publisher Savvas Learning Co
• Publication date January 1, 2011
• Dimensions 8.19 x 0.71 x 10.71 inches
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• ASIN ‏ : ‎ 0133185966
• Publisher ‏ : ‎ Savvas Learning Co; 3/15/11 edition (January 1, 2011)
• Language ‏ : ‎ English
• ISBN-10 ‏ : ‎ 9780133185966
• ISBN-13 ‏ : ‎ 978-0133185966
• Item Weight ‏ : ‎ 7.7 ounces
• Dimensions ‏ : ‎ 8.19 x 0.71 x 10.71 inches
• #690 in Decision-Making & Problem Solving

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There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

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Title: learning to solve geometry problems via simulating human dual-reasoning process.

Abstract: Geometry Problem Solving (GPS), which is a classic and challenging math problem, has attracted much attention in recent years. It requires a solver to comprehensively understand both text and diagram, master essential geometry knowledge, and appropriately apply it in reasoning. However, existing works follow a paradigm of neural machine translation and only focus on enhancing the capability of encoders, which neglects the essential characteristics of human geometry reasoning. In this paper, inspired by dual-process theory, we propose a Dual-Reasoning Geometry Solver (DualGeoSolver) to simulate the dual-reasoning process of humans for GPS. Specifically, we construct two systems in DualGeoSolver, namely Knowledge System and Inference System. Knowledge System controls an implicit reasoning process, which is responsible for providing diagram information and geometry knowledge according to a step-wise reasoning goal generated by Inference System. Inference System conducts an explicit reasoning process, which specifies the goal in each reasoning step and applies the knowledge to generate program tokens for resolving it. The two systems carry out the above process iteratively, which behaves more in line with human cognition. We conduct extensive experiments on two benchmark datasets, GeoQA and GeoQA+. The results demonstrate the superiority of DualGeoSolver in both solving accuracy and robustness from explicitly modeling human reasoning process and knowledge application.

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Unit 1: Algebra foundations

Unit 2: solving equations & inequalities, unit 3: working with units, unit 4: linear equations & graphs, unit 5: forms of linear equations, unit 6: systems of equations, unit 7: inequalities (systems & graphs), unit 8: functions, unit 9: sequences, unit 10: absolute value & piecewise functions, unit 11: exponents & radicals, unit 12: exponential growth & decay, unit 13: quadratics: multiplying & factoring, unit 14: quadratic functions & equations, unit 15: irrational numbers, unit 16: creativity in algebra.