# High School Geometry

**Relevant Brilliant Courses (Online Content)**

The four courses below are the foundations for all of the mathematics offered on Brilliant. If you’re an educator with a group of 10 or more students you want to give full access to these courses, contact pricing@brilliant.org to learn more about Brilliant’s discounts for school groups.

**Deep Diving Math Enrichment Problem Sets (Printable Content)**

Too often, school math is all about “racing to finish” instead of diving deep to understand and explore creative, tangential lines of inquiry. These sets were written to inspire deep diving exploration that extends and enriches the core mathematical topics and skills introduced in the geometry common core curriculum.

Each of the “Practice-Challenge-Culmination” problem sets listed below takes some foundational skill in the common core curriculum for that grade and, after a few practice problems, extends the concept to more creative challenges, and then to a single, deep-dive question.

#### Contents

## Quadrilaterals and Other Polygons

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentPROOFS: PEGBOARD RECTANGLES [Printable PDF] CCSS.MATH.CONTENT.HSA.CED.A.2 CCSS.MATH.CONTENT.HSG.MG.A.3 This is a tightly sequenced set that has a geometry proof of an algebraic nature: the case of Pick's Theorem that involves only unit squares. It is more of a structured exploration than some of the other tasks; problems rely on answers to previous problems. Because of the structure, the students should be exposed to the goal (the “culmination”) before they start any of the problems. Out Of The Box Geometry: Pegboard Triangles REGULAR POLYGONS [Printable PDF] CCSS.MATH.CONTENT.HSG.SRT.B.4 CCSS.MATH.CONTENT.HSG.SRT.B.5 CCSS.MATH.CONTENT.HSG.SRT.C.8 This includes a mixed set of problems involving area, perimeter and angles of regular polygons. 30-60-90 triangles are used in the culmination question. Out Of The Box Geometry: Triangles and Hexagons

## Lines and Angle Relationships

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentANGLES WITH PARALLEL LINES [Printable PDF] CCSS.MATH.CONTENT.HSG.CO.C.9 CCSS.MATH.CONTENT.HSG.CO.C.11 CCSS.MATH.CONTENT.HSA.REI.B.3 This set of angle-solving problems apply parallel lines in creative ways; the hardest problem involves exploration and proof with parallelograms. Out of the Box Geometry: Angle Hunting Axioms

## Area, Surface Area, and Volume

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentCOMPOSITE GEOMETRY [Printable PDF] CCSS.MATH.CONTENT.HSG.CO.B.6 CCSS.MATH.PRACTICE.MP1 CCSS.MATH.PRACTICE.MP7 These problems explore the geometry of composite figures. Composite figures are created by combining bits and pieces of basic figures, such as circles, rectangles, and triangles. Students can be creative about problem solving strategies. This exploration allows for a wide variation in skill level, and any strategy for finding a solution to these puzzles is valid, as long as the student can explain why it works! Mathematical Fundamentals: Challenging Composites

## Triangle Relationships

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentPROOF: ANGLE BISECTOR THEOREM [Printable PDF] CCSS.MATH.CONTENT.HSG.SRT.B.4 CCSS.MATH.CONTENT.HSG.SRT.B.5 This series of problems leads to a proof of the angle bisector theorem, and then a tricky problem that applies it! Before starting, students should know these terms: angle bisector, median, altitude and perpendicular bisector. The intent for these problems is that students produce proofs rather than just answers. The full angle bisector theorem should be extracted from the second challenging problem before moving to the (very tricky!) culmination problem. Outside of the Box Geometry: Cevians TRIANGLE CLASSIFICATION [Printable PDF] CCSS.MATH.CONTENT.HSG.SRT.B.4 CCSS.MATH.CONTENT.HSG.SRT.C.8 This series includes some creative problems involving identifying the different triangle types and using them in context. The harder problems involve finding different triangle types on a pegboard and on a cube. Outside of the Box Geometry: Pegboard Triangles TRIANGLE CONGRUENCE [Printable PDF] CCSS.MATH.CONTENT.HSG.SRT.B.4 CCSS.MATH.CONTENT.HSG.SRT.B.5 CCSS.MATH.CONTENT.HSG.SRT.C.8 This series includes problem solving related to ASA, SSS, and AAS congruence, as well as the two possible triangles in the SSA case. Note the Pythagorean theorem and 30-60-90 triangles also make an appearance. Outside of the Box Geometry: Congruence and Similarity TRIANGLE SIMILARITY [Printable PDF] CCSS.MATH.CONTENT.HSG.SRT.A.2 CCSS.MATH.CONTENT.HSG.SRT.A.3 CCSS.MATH.CONTENT.HSG.SRT.B.5 These problems include multiple perspectives on triangle similarity, including calculations on side lengths and area. The culmination problem connects similarity to fractals. Mathematical Fundamentals: Similarity

## Similarity, Congruence, and Transformations

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentSIMILARITY SCALING [Printable PDF] CCSS.MATH.CONTENT.HSG.SRT.A.2 CCSS.MATH.CONTENT.HSG.SRT.B.5 These are similarity problems with an emphasis on how applying a scale factor to the sides affects the area or volume. Mathematical Fundamentals: Scaling

## Right Triangles and Trigonometry

Printable PDFsCommon Core StandardsDescriptionRelated Course ContentPYTHAGOREAN THEOREM PROOFS [Printable PDF] CCSS.MATH.CONTENT.HSG.SRT.B.4 CCSS.MATH.CONTENT.HSG.SRT.B.5 This special series of problems explores different proofs of the Pythagorean Theorem. It includes extensive use of algebra and similarity. Outside of the Box Geometry: Right Triangles

## Properties of Circles

Coming Soon

**Cite as:**High School Geometry.

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