Public learning track
Geometric Constructions and Triangle Inequalities
6th Grade · Math · Open Global Math
8 lessons
Goal
Construct triangles and geometric figures with compass and straightedge, apply the triangle inequality theorem, and construct angle and segment bisectors.
Featured Diagrams
Applying the Triangle Inequality Theorem to Solve Problems
8 lessons
0 of 8 done
- 1Applying the Triangle Inequality Theorem to Solve ProblemsUp nextStart
- 2Finding the Range of Possible Third Side Lengths in a TrianglePremiumNot started yet
- 3Constructing Triangles Given Three Side Lengths (SSS)Not started yet
- 4Constructing Triangles Given SAS and ASA ConditionsNot started yet
- 5Drawing Triangles from Three Angle MeasuresNot started yet
- 6Constructing Perpendicular Bisectors of Line SegmentsNot started yet
- 7Constructing Angle Bisectors with Compass and StraightedgeNot started yet
- 8Drawing Polygons with Specified Side and Angle PropertiesNot started yet
Standards Covered
- OGM.7.GEO.7Open Global Math Standards 2026™ · Math · Level 7 / Grade 6 (Age 11) · Grade 6Investigate properties of triangles and quadrilaterals: apply the triangle inequality theorem (a + b > c), use the interior angle sum theorem (180° for triangles, 360° for quadrilaterals, (n-2)·180° for n-gons), and classify polygons by side lengths and angle measures.
- OGM.7.GEO.8Open Global Math Standards 2026™ · Math · Level 7 / Grade 6 (Age 11) · Grade 6Perform and analyze rigid transformations (translations, rotations, reflections) and dilations (enlargements/reductions with scale factors) on coordinate grids; construct line and rotational symmetry, perpendicular bisectors, angle bisectors, and analyze tessellations.
Curriculum Framework
6th Grade · Math · Open Global Math
1
10 lessons
Angle Relationships and Geometric Reasoning
Identify, classify, and calculate unknown angle measures using complementary, supplementary, vertical, adjacent, and intersecting line relationships with algebraic equations.
2
11 lessons
Triangles, Polygons, and Angle Theorems
Investigate, classify, and calculate interior and exterior angle sums for triangles, special quadrilaterals, and regular and irregular n-gons.
3
8 lessons
Geometric Constructions and Triangle Inequalities
Construct triangles and geometric figures with compass and straightedge, apply the triangle inequality theorem, and construct angle and segment bisectors.
4
10 lessons
Area and Perimeter of Two-Dimensional Polygons
Derive and apply formulas for perimeter and area of triangles, parallelograms, rhombuses, and trapezoids with consistent metric and customary units.
5
7 lessons
Decomposing Figures and Composite Area
Calculate the area of complex, composite, and irregular 2D polygons by additive composition and subtractive decomposition.
6
11 lessons
Circles: Circumference, Area, and Circular Rings
Identify parts of a circle, derive the constant ratio pi (π = C/d), and calculate circumference, circle area, sector angles, and annulus ring areas.
7
10 lessons
Cartesian Coordinate Plane: Distances and Polygons
Plot points in all four quadrants, calculate horizontal and vertical segment lengths using absolute value, and construct polygons to determine coordinate perimeter and area.
8
8 lessons
Rigid Transformations on the Coordinate Plane
Perform, describe, and analyze translations, reflections, and rotations of 2D shapes on coordinate grids using algebraic mapping rules.
9
7 lessons
Dilations, Scale Factors, and Similarity
Perform and analyze dilations centered at the origin or arbitrary points, calculate scale factors, and explore properties of similar geometric figures.
10
7 lessons
Symmetry Transformations and Tessellations
Analyze line and rotational symmetry in 2D shapes, determine orders of rotation, and investigate regular, semi-regular, and artistic tessellations.
11
7 lessons
Three-Dimensional Solids, Cross-Sections, and Views
Identify 3D solid structures, interpret and draw 2D orthographic projections (top, front, side), and determine shapes formed by 2D cross-sections.
12
7 lessons
Scale Drawings, Maps, and Bearings
Construct and interpret scale drawings, architectural floor plans, map routes, three-figure bearings, and cardinal directional bearings.
13
9 lessons
Two-Dimensional Nets and Surface Area of Solids
Unfold 3D solids into 2D nets and calculate total and lateral surface areas of rectangular prisms, triangular prisms, pyramids, and cylinders.
14
8 lessons
Volume of Prisms, Unit Cubes, and Capacity Conversions
Calculate the volume of cubes and right rectangular prisms with fractional and decimal edges using packing and formulas, and convert between cubic volume and liquid capacity.