# Geometry and spatial reasoning

See recommended skills!Here is a list of all of the skills that cover geometry and spatial reasoning! These skills are organized by grade, and you can move your mouse over any skill name to view a sample question. To start practicing, just click on any link. IXL will track your score, and the questions will automatically increase in difficulty as you improve!

## Pre-K skills

- F.1Inside and outside
- F.2Left and right
- F.3Left, middle, and right
- F.4Top and bottom
- F.5Top, middle, and bottom
- F.6Above and below
- F.7Beside and next to
- K.1Name the shape
- K.2Circles
- K.3Squares
- K.4Triangles
- K.5Circles, squares, and triangles
- L.1Flat and solid shapes
- L.2Name the solid shape
- L.3Spheres
- L.4Cubes
- L.5Cones
- L.6Cylinders
- L.7Select solid shapes

## Kindergarten skills

- M.1Inside and outside
- M.2Left, middle, and right
- M.3Top, middle, and bottom
- M.4Location in a grid
- M.5Above and below
- M.6Above and below - find solid figures
- M.7Beside and next to
- M.8Beside and next to - find solid figures
- P.8Count shapes in a Venn diagram
- P.9Sort shapes into a Venn diagram
- V.1Name the two-dimensional shape
- V.2Circles
- V.3Squares and rectangles
- V.4Hexagons
- V.5Select two-dimensional shapes
- V.6Count sides and corners
- V.7Compare sides and corners
- V.8Introduction to symmetry
- V.9Identify pictures with symmetry
- W.1Two-dimensional and three-dimensional shapes
- W.2Name the three-dimensional shape
- W.3Spheres
- W.4Cubes
- W.5Cones
- W.6Cylinders
- W.7Select three-dimensional shapes
- W.8Identify shapes traced from solids
- W.9Shapes of everyday objects I
- W.10Shapes of everyday objects II

## First-grade skills

- N.1Left, middle, and right
- N.2Top, middle, and bottom
- N.3Location in a grid
- N.4Above and below
- N.5Beside and next to
- T.1Count shapes in a Venn diagram
- T.2Sort shapes into a Venn diagram
- V.1Name the two-dimensional shape
- V.2Select two-dimensional shapes
- V.3Count sides and vertices
- V.4Compare sides and vertices
- V.5Open and closed shapes
- V.6Flip, turn, and slide
- V.7Symmetry
- W.1Two-dimensional and three-dimensional shapes
- W.2Name the three-dimensional shape
- W.3Cubes and rectangular prisms
- W.4Select three-dimensional shapes
- W.5Count vertices, edges, and faces
- W.6Compare vertices, edges, and faces
- W.7Identify shapes traced from solids
- W.8Identify faces of three-dimensional shapes
- W.9Shapes of everyday objects I
- W.10Shapes of everyday objects II

## Second-grade skills

- R.11Count shapes in a Venn diagram
- R.12Sort shapes into a Venn diagram
- T.1Name the two-dimensional shape
- T.2Select two-dimensional shapes
- T.3Count sides and vertices
- T.4Compare sides and vertices
- T.5Flip, turn, and slide
- T.6Identify congruent shapes
- T.7Symmetry
- U.1Name the three-dimensional shape
- U.2Select three-dimensional shapes
- U.3Count vertices, edges, and faces
- U.4Compare vertices, edges, and faces
- U.5Identify faces of three-dimensional shapes
- U.6Identify shapes traced from solids
- U.7Shapes of everyday objects I
- U.8Shapes of everyday objects II
- V.1Perimeter
- V.2Perimeter - word problems
- V.3Find the area of figures made of unit squares
- V.4Create figures with a given area

## Third-grade skills

- U.13Count shapes in a Venn diagram
- U.14Sort shapes into a Venn diagram
- CC.1Identify two-dimensional shapes
- CC.2Count and compare sides and vertices
- CC.3Open and closed shapes
- CC.4Is it a polygon?
- CC.5Lines, line segments, and rays
- CC.6Angles greater than, less than, or equal to a right angle
- CC.7Parallel, perpendicular, and intersecting lines
- CC.8Reflection, rotation, and translation
- CC.9Identify congruent shapes
- CC.10Symmetry
- DD.1Acute, obtuse, and right triangles
- DD.2Scalene, isosceles, and equilateral triangles
- DD.3Classify quadrilaterals
- DD.4Properties of triangles and quadrilaterals
- EE.1Identify three-dimensional shapes
- EE.2Count vertices, edges, and faces
- EE.3Identify faces of three-dimensional shapes
- EE.4Shapes of everyday objects I
- EE.5Shapes of everyday objects II
- FF.1Perimeter
- FF.2Perimeter: find the missing side length
- FF.3Perimeter: word problems
- FF.4Find the area of figures made of unit squares
- FF.5Create figures with a given area
- FF.6Find the area of rectangles and squares
- FF.7Find the missing side length of a rectangle
- FF.8Find the area of rectangles: word problems
- FF.9Find the area of complex figures
- FF.10Find the area between two rectangles
- FF.11Compare area and perimeter of two figures
- FF.12Use area and perimeter to determine cost
- FF.13Relationship between area and perimeter
- FF.14Volume

## Fourth-grade skills

- W.1Open and closed shapes
- W.2Is it a polygon?
- W.3Number of sides in polygons
- W.4Lines, line segments, and rays
- W.5Parallel, perpendicular, and intersecting lines
- W.6Identify congruent figures
- W.7Parts of a circle
- X.1Acute, obtuse, and right triangles
- X.2Scalene, isosceles, and equilateral triangles
- X.3Classify triangles
- X.4Classify quadrilaterals
- X.5Properties of triangles and quadrilaterals
- Y.1Identify lines of symmetry
- Y.2Draw lines of symmetry
- Y.3Count lines of symmetry
- Y.4Rotational symmetry
- Z.1Acute, right, obtuse, and straight angles
- Z.2Angles of 90, 180, 270, and 360 degrees
- Z.3Measure angles with a protractor
- Z.4Estimate angle measurements
- Z.5Adjacent angles
- AA.1Identify three-dimensional figures
- AA.2Count vertices, edges, and faces
- AA.3Identify faces of three-dimensional figures
- AA.4Properties of three-dimensional figures
- AA.5Nets of three-dimensional figures
- BB.1Perimeter
- BB.2Create figures with a given area
- BB.3Find the area or missing side length of a rectangle
- BB.4Area of complex figures (with all right angles)
- BB.5Area between two rectangles
- BB.6Compare area and perimeter of two figures
- BB.7Relationship between area and perimeter
- BB.8Area and perimeter: word problems
- BB.9Volume
- BB.10Use area and perimeter to determine cost
- BB.11Calculate radius, diameter, and circumference

## Fifth-grade skills

- AA.1Is it a polygon?
- AA.2Number of sides in polygons
- AA.3Regular and irregular polygons
- AA.4Lines, line segments, and rays
- AA.5Parallel, perpendicular, and intersecting lines
- AA.6Types of angles
- AA.7Measure angles with a protractor
- AA.8Find the unknown angle in triangles and quadrilaterals
- AA.9Parts of a circle
- BB.1Acute, obtuse, and right triangles
- BB.2Scalene, isosceles, and equilateral triangles
- BB.3Classify triangles
- BB.4Classify quadrilaterals
- BB.5Properties of triangles and quadrilaterals
- CC.1Lines of symmetry
- CC.2Rotational symmetry
- CC.3Reflection, rotation, and translation
- CC.4Identify congruent and similar figures
- DD.1Identify three-dimensional figures
- DD.2Count vertices, edges, and faces
- DD.3Nets of three-dimensional figures
- DD.4Three-dimensional figures viewed from different perspectives
- EE.1Perimeter
- EE.2Area of squares and rectangles
- EE.3Area of triangles
- EE.4Area of parallelograms and trapezoids
- EE.5Area of compound figures
- EE.6Area between two rectangles
- EE.7Area and perimeter of figures on grids
- EE.8Area and perimeter: word problems
- EE.9Volume of rectangular prisms made of unit cubes
- EE.10Volume of irregular figures made of unit cubes
- EE.11Volume of cubes and rectangular prisms
- EE.12Surface area
- EE.13Radius, diameter, circumference, and area of a circle

## Sixth-grade skills

- X.5Distance between two points
- CC.1Identify and classify polygons
- CC.2Measure and classify angles
- CC.3Estimate angle measurements
- CC.4Classify triangles
- CC.5Classify quadrilaterals
- CC.6Graph triangles and quadrilaterals
- CC.7Find missing angles in triangles and quadrilaterals
- CC.8Sums of angles in polygons
- CC.9Lines, line segments, and rays
- CC.10Name angles
- CC.11Complementary and supplementary angles
- CC.12Transversal of parallel lines
- CC.13Find lengths and measures of bisected lines and angles
- CC.14Parts of a circle
- CC.15Central angles of circles
- DD.1Symmetry
- DD.2Reflection, rotation, and translation
- DD.3Translations: graph the image
- DD.4Reflections: graph the image
- DD.5Rotations: graph the image
- DD.6Similar and congruent figures
- DD.7Find side lengths of similar figures
- EE.1Identify polyhedra
- EE.2Which figure is being described?
- EE.3Nets of three-dimensional figures
- EE.4Front, side, and top view
- FF.1Perimeter
- FF.2Area of rectangles and squares
- FF.3Area of triangles
- FF.4Area of parallelograms and trapezoids
- FF.5Area of quadrilaterals
- FF.6Area of compound figures
- FF.7Area between two rectangles
- FF.8Area between two triangles
- FF.9Rectangles: relationship between perimeter and area
- FF.10Compare area and perimeter of two figures
- FF.11Circles: calculate area, circumference, radius, and diameter
- FF.12Circles: word problems
- FF.13Area between two circles
- FF.14Volume of cubes and rectangular prisms
- FF.15Surface area of cubes and rectangular prisms
- FF.16Volume and surface area of triangular prisms
- FF.17Volume and surface area of cylinders
- FF.18Relate volume and surface area
- FF.19Semicircles: calculate area, perimeter, radius, and diameter
- FF.20Quarter circles: calculate area, perimeter, and radius
- FF.21Area of compound figures with triangles, semicircles, and quarter circles

## Seventh-grade skills

- P.4Distance between two points
- W.1Identify and classify polygons
- W.2Name, measure, and classify angles
- W.3Classify triangles
- W.4Classify quadrilaterals
- W.5Graph triangles and quadrilaterals
- W.6Find missing angles in triangles and quadrilaterals
- W.7Interior angles of polygons
- W.8Lines, line segments, and rays
- W.9Parallel, perpendicular, and intersecting lines
- W.10Identify complementary, supplementary, vertical, adjacent, and congruent angles
- W.11Find measures of complementary, supplementary, vertical, and adjacent angles
- W.12Transversal of parallel lines
- W.13Find lengths and measures of bisected lines and angles
- W.14Parts of a circle
- X.1Symmetry
- X.2Identify reflections, rotations, and translations
- X.3Translations: graph the image
- X.4Translations: find the coordinates
- X.5Reflections: graph the image
- X.6Reflections: find the coordinates
- X.7Rotations: graph the image
- X.8Rotations: find the coordinates
- X.9Similar and congruent figures
- X.10Congruence statements and corresponding parts
- X.11Side lengths and angle measures of congruent figures
- X.12Side lengths and angle measures of similar figures
- X.13Similar figures and indirect measurement
- Y.1Pythagorean theorem: find the length of the hypotenuse
- Y.2Pythagorean theorem: find the missing leg length
- Y.3Pythagorean theorem: word problems
- Y.4Converse of the Pythagorean theorem: is it a right triangle?
- Z.1Bases of three-dimensional figures
- Z.2Nets of three-dimensional figures
- Z.3Front, side, and top view
- AA.1Perimeter
- AA.2Area of rectangles and parallelograms
- AA.3Area of triangles and trapezoids
- AA.4Area and perimeter: word problems
- AA.5Circles: calculate area, circumference, radius, and diameter
- AA.6Circles: word problems
- AA.7Volume
- AA.8Surface area
- AA.9Perimeter, area, and volume: changes in scale
- AA.10Semicircles: calculate area, perimeter, radius, and diameter
- AA.11Quarter circles: calculate area, perimeter, and radius
- AA.12Area of compound figures with triangles, semicircles, and quarter circles
- AA.13Area between two shapes

## Eighth-grade skills

- N.4Find the distance between two points
- O.1Identify and classify polygons
- O.2Classify triangles
- O.3Classify quadrilaterals
- O.4Graph triangles and quadrilaterals
- O.5Find missing angles in triangles and quadrilaterals
- O.6Exterior Angle Theorem
- O.7Interior angles of polygons
- O.8Identify complementary, supplementary, vertical, adjacent, and congruent angles
- O.9Find measures of complementary, supplementary, vertical, and adjacent angles
- O.10Transversal of parallel lines
- O.11Find lengths and measures of bisected lines and angles
- O.12Parts of a circle
- P.1Symmetry
- P.2Identify reflections, rotations, and translations
- P.3Translations: graph the image
- P.4Translations: find the coordinates
- P.5Reflections: graph the image
- P.6Reflections: find the coordinates
- P.7Rotations: graph the image
- P.8Rotations: find the coordinates
- P.9Congruence statements and corresponding parts
- P.10Side lengths and angle measures of congruent figures
- P.11Congruent triangles: SSS, SAS, and ASA
- Q.1Similar and congruent figures
- Q.2Dilations: graph the image
- Q.3Dilations: find the coordinates
- Q.4Dilations: scale factor and classification
- Q.5Side lengths and angle measures of similar figures
- R.1Pythagorean theorem: find the length of the hypotenuse
- R.2Pythagorean theorem: find the missing leg length
- R.3Pythagorean theorem: find the perimeter
- R.4Pythagorean theorem: word problems
- R.5Converse of the Pythagorean theorem: is it a right triangle?
- S.1Parts of 3-dimensional figures
- S.2Nets of three-dimensional figures
- S.3Front, side, and top view
- S.4Base plans
- S.5Similar solids
- T.1Perimeter
- T.2Area
- T.3Area and perimeter: word problems
- T.4Area between two shapes
- T.5Circles, semicircles, and quarter circles
- T.6Circles: word problems
- T.7Volume of cubes, prisms, and pyramids
- T.8Surface area of cubes, prisms, and pyramids
- T.9Volume of cylinders and cones
- T.10Surface area of cylinders and cones
- T.11Volume of spheres
- T.12Surface area of spheres
- T.13Volume and surface area of similar solids
- T.14Perimeter, area, and volume: changes in scale
- BB.5Add polynomials to find perimeter
- BB.13Multiply polynomials to find area

## Algebra 1 skills

- E.6Minimum and maximum area and volume
- E.8Percent error: area and volume
- F.1Perimeter
- F.2Area
- F.3Area and perimeter: word problems
- F.4Volume
- F.5Surface area
- F.6Similar figures: side lengths and angle measures
- F.7Similar triangles and indirect measurement
- F.8Dilations and scale factors
- F.9Area and perimeter of similar figures
- F.10Area between two shapes
- F.11Similar solids
- F.12Volume and surface area of similar solids
- F.13Perimeter, area, and volume: changes in scale
- F.14Pythagorean theorem
- F.15Pythagorean theorem: word problems
- F.16Converse of the Pythagorean theorem: is it a right triangle?
- F.17Special right triangles
- G.2Midpoints
- G.3Distance between two points
- Z.5Add polynomials to find perimeter
- HH.1Trigonometric ratios: sin, cos, and tan
- HH.2Find trigonometric ratios using a calculator
- HH.3Inverses of trigonometric functions
- HH.4Trigonometric ratios: find a side length
- HH.5Trigonometric ratios: find an angle measure
- HH.6Solve a right triangle

## Geometry skills

- B.1Lines, line segments, and rays
- B.2Lengths of segments on number lines
- B.3Additive property of length
- B.4Midpoints
- B.5Congruent line segments
- B.6Perpendicular Bisector Theorem
- B.7Midpoint formula
- B.8Distance formula
- B.9Construct the midpoint or perpendicular bisector of a segment
- C.1Angle vocabulary
- C.2Angle measures
- C.3Identify complementary, supplementary, vertical, adjacent, and congruent angles
- C.4Find measures of complementary, supplementary, vertical, and adjacent angles
- C.5Angle bisectors
- C.6Construct an angle bisector
- C.7Construct a congruent angle
- C.8Proofs involving angles
- D.1Identify parallel, perpendicular, and skew lines and planes
- D.2Construct a perpendicular line
- D.3Transversals: name angle pairs
- D.4Transversals of parallel lines: find angle measures
- D.5Construct parallel lines
- D.6Proofs involving parallel lines I
- D.7Proofs involving parallel lines II
- E.7Find the distance between a point and a line
- E.8Find the distance between two parallel lines
- F.1Classify triangles
- F.2Triangle Angle-Sum Theorem
- F.3Exterior Angle Theorem
- F.4Exterior Angle Inequality
- G.1Polygon vocabulary
- G.2Interior angles of polygons
- G.3Exterior angles of polygons
- G.4Review: interior and exterior angles of polygons
- G.5Construct an equilateral triangle or regular hexagon
- G.6Construct a square
- H.1Parts of three-dimensional figures
- H.2Three-dimensional figure vocabulary
- H.3Nets and drawings of three-dimensional figures
- H.4Cross-sections of three-dimensional figures
- H.5Solids of revolution
- J.1Congruence statements and corresponding parts
- J.2Solve problems involving corresponding parts
- J.3Identify congruent figures
- K.1SSS and SAS Theorems
- K.2Proving triangles congruent by SSS and SAS
- K.3ASA and AAS Theorems
- K.4Proving triangles congruent by ASA and AAS
- K.5SSS, SAS, ASA, and AAS Theorems
- K.6SSS Theorem in the coordinate plane
- K.7Proving triangles congruent by SSS, SAS, ASA, and AAS
- K.8Proofs involving corresponding parts of congruent triangles
- K.9Congruency in isosceles and equilateral triangles
- K.10Proofs involving isosceles triangles
- K.11Hypotenuse-Leg Theorem
- L.1Classify congruence transformations
- L.2Translations: graph the image
- L.3Translations: find the coordinates
- L.4Translations: write the rule
- L.5Reflections: graph the image
- L.6Reflections: find the coordinates
- L.7Rotate polygons about a point
- L.8Rotations: graph the image
- L.9Rotations: find the coordinates
- L.10Compositions of congruence transformations: graph the image
- L.11Transformations that carry a polygon onto itself
- L.12Congruence transformations: mixed review
- L.13Dilations: graph the image
- L.14Dilations: find the coordinates
- L.15Dilations: scale factor and classification
- L.16Dilations and parallel lines
- M.1Midsegments of triangles
- M.2Triangles and bisectors
- M.3Identify medians, altitudes, angle bisectors, and perpendicular bisectors
- M.4Angle-side relationships in triangles
- M.5Triangle Inequality Theorem
- M.6Construct the circumcenter or incenter of a triangle
- M.7Construct the centroid or orthocenter of a triangle
- M.8Proofs involving triangles I
- M.9Proofs involving triangles II
- N.1Classify quadrilaterals
- N.2Graph quadrilaterals
- N.3Properties of parallelograms
- N.4Proving a quadrilateral is a parallelogram
- N.5Properties of rhombuses
- N.6Properties of squares and rectangles
- N.7Properties of trapezoids
- N.8Properties of kites
- N.9Review: properties of quadrilaterals
- N.10Proofs involving quadrilaterals I
- N.11Proofs involving quadrilaterals II
- O.1Line symmetry
- O.2Rotational symmetry
- O.3Draw lines of symmetry
- O.4Count lines of symmetry
- P.1Similarity ratios
- P.2Similarity statements
- P.3Identify similar figures
- P.4Side lengths and angle measures in similar figures
- P.5Similar triangles and indirect measurement
- P.6Perimeters of similar figures
- P.7Similarity rules for triangles
- P.8Similar triangles and similarity transformations
- P.9Similarity of circles
- P.10Triangle Proportionality Theorem
- P.11Areas of similar figures
- Q.1Pythagorean Theorem
- Q.2Converse of the Pythagorean theorem
- Q.3Pythagorean Inequality Theorems
- Q.4Special right triangles
- R.1Trigonometric ratios: sin, cos, and tan
- R.2Trigonometric ratios: csc, sec, and cot
- R.3Trigonometric ratios in similar right triangles
- R.4Trigonometric functions of complementary angles
- R.5Find trigonometric functions of special angles
- R.6Find trigonometric functions using a calculator
- R.7Inverses of trigonometric functions
- R.8Trigonometric ratios: find a side length
- R.9Trigonometric ratios: find an angle measure
- R.10Solve a right triangle
- R.11Law of Sines
- R.12Law of Cosines
- R.13Solve a triangle
- S.1Perimeter
- S.2Area of rectangles and squares
- S.3Area of parallelograms and triangles
- S.4Area of trapezoids
- S.5Area and perimeter in the coordinate plane I
- S.6Area and perimeter in the coordinate plane II
- S.7Area and circumference of circles
- S.8Area of compound figures
- S.9Area between two shapes
- S.10Area and perimeter of similar figures
- S.11Heron's formula
- S.12Area and perimeter mixed review
- T.1Introduction to surface area and volume
- T.2Surface area of prisms and cylinders
- T.3Surface area of pyramids and cones
- T.4Volume of prisms and cylinders
- T.5Volume of pyramids and cones
- T.6Surface area and volume of spheres
- T.7Introduction to similar solids
- T.8Surface area and volume of similar solids
- T.9Surface area and volume review
- U.1Parts of a circle
- U.2Central angles
- U.3Arc measure and arc length
- U.4Area of sectors
- U.5Circle measurements: mixed review
- U.6Arcs and chords
- U.7Tangent lines
- U.8Perimeter of polygons with an inscribed circle
- U.9Inscribed angles
- U.10Angles in inscribed right triangles
- U.11Angles in inscribed quadrilaterals
- U.12Construct a tangent line to a circle
- U.13Construct an equilateral triangle inscribed in a circle
- U.14Construct a square inscribed in a circle
- U.15Construct a regular hexagon inscribed in a circle
- U.16Construct the inscribed or circumscribed circle of a triangle
- V.1Find the center of a circle
- V.2Find the radius or diameter of a circle
- V.3Write equations of circles in standard form from graphs
- V.4Write equations of circles in standard form using properties
- V.5Graph circles
- W.6Minimum and maximum area and volume
- W.8Percent error: area and volume
- X.7Geometric probability
- Y.1Compass directions and vectors
- Y.2Find the magnitude of a vector
- Y.3Find the component form of a vector
- Y.4Find the component form of a vector given its magnitude and direction angle
- Y.5Graph a resultant vector using the triangle method
- Y.6Graph a resultant vector using the parallelogram method
- Y.7Add and subtract vectors

## Algebra 2 skills

- T.1Identify the direction a parabola opens
- T.2Find the vertex of a parabola
- T.3Find the focus or directrix of a parabola
- T.4Find the axis of symmetry of a parabola
- T.5Write equations of parabolas in vertex form from graphs
- T.6Write equations of parabolas in vertex form using properties
- T.7Convert equations of parabolas from general to vertex form
- T.8Find properties of a parabola from equations in general form
- T.9Graph parabolas
- U.1Find the center of a circle
- U.2Find the radius or diameter of a circle
- U.3Write equations of circles in standard form from graphs
- U.4Write equations of circles in standard form using properties
- U.5Convert equations of circles from general to standard form
- U.6Find properties of circles from equations in general form
- U.7Graph circles
- V.1Find the center, vertices, or co-vertices of an ellipse
- V.2Find the length of the major or minor axes of an ellipse
- V.3Find the foci of an ellipse
- V.4Write equations of ellipses in standard form from graphs
- V.5Write equations of ellipses in standard form using properties
- V.6Convert equations of ellipses from general to standard form
- V.7Find properties of ellipses from equations in general form
- W.1Find the center of a hyperbola
- W.2Find the vertices of a hyperbola
- W.3Find the length of the transverse or conjugate axes of a hyperbola
- W.4Find the equations for the asymptotes of a hyperbola
- W.5Find the foci of a hyperbola
- W.6Write equations of hyperbolas in standard form from graphs
- W.7Write equations of hyperbolas in standard form using properties
- W.8Convert equations of hyperbolas from general to standard form
- W.9Find properties of hyperbolas from equations in general form
- X.1Convert between radians and degrees
- X.2Radians and arc length
- X.5Coterminal angles
- X.6Reference angles
- Y.1Pythagorean Theorem and its converse
- Y.2Special right triangles
- Y.3Trigonometric ratios: sin, cos, and tan
- Y.4Trigonometric ratios: csc, sec, and cot
- Y.5Trigonometric ratios in similar right triangles
- Y.6Find trigonometric ratios using the unit circle
- Y.7Sin, cos, and tan of special angles
- Y.9Find trigonometric functions using a calculator
- Y.10Inverses of sin, cos, and tan
- Y.12Solve trigonometric equations I
- Y.13Solve trigonometric equations II
- Y.14Trigonometric ratios: find a side length
- Y.15Trigonometric ratios: find an angle measure
- Y.16Solve a right triangle
- Y.17Law of Sines
- Y.18Law of Cosines
- Y.19Solve a triangle
- Y.20Area of a triangle: sine formula
- Y.21Area of a triangle: Law of Sines
- AA.1Complementary angle identities
- AA.2Symmetry and periodicity of trigonometric functions

## Precalculus skills

- M.1Convert between radians and degrees
- M.2Radians and arc length
- M.4Coterminal and reference angles
- M.5Find trigonometric ratios using right triangles
- M.6Find trigonometric ratios using the unit circle
- M.8Inverses of trigonometric functions
- M.9Solve trigonometric equations
- M.10Trigonometric ratios: find a side length
- M.11Trigonometric ratios: find an angle measure
- M.12Solve a right triangle
- M.13Law of Sines
- M.14Law of Cosines
- M.15Solve a triangle
- M.16Area of a triangle: sine formula
- M.17Area of a triangle: Heron's formula
- O.1Complementary angle identities
- O.2Symmetry and periodicity of trigonometric functions
- P.1Find properties of parabolas
- P.2Write equations of parabolas in vertex form
- P.3Graph parabolas
- P.4Find properties of circles
- P.5Write equations of circles in standard form
- P.6Graph circles
- P.7Find properties of ellipses
- P.8Find the eccentricity of an ellipse
- P.9Write equations of ellipses in standard form
- P.10Find properties of hyperbolas
- P.11Find the eccentricity of a hyperbola
- P.12Write equations of hyperbolas in standard form
- P.13Convert equations of conic sections from general to standard form
- S.8Distance in the complex plane
- U.1Find the magnitude of a vector
- U.2Find the component form of a vector
- U.3Find the direction angle of a vector
- U.4Find the component form of a vector from its magnitude and direction angle
- U.5Graph a resultant vector using the triangle method
- U.6Graph a resultant vector using the parallelogram method
- U.7Add and subtract vectors
- U.8Find the magnitude and direction of a vector sum
- U.9Multiply a vector by a scalar
- U.10Find the magnitude or direction of a vector scalar multiple
- U.11Find a unit vector
- U.12Linear combinations of vectors
- V.1Find the magnitude of a three-dimensional vector
- V.2Find the component form of a three-dimensional vector
- V.3Add and subtract three-dimensional vectors
- V.4Scalar multiples of three-dimensional vectors
- V.5Find a three-dimensional unit vector
- V.6Linear combinations of three-dimensional vectors