# Geometry

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

## Junior-infants skills

- F.1Inside and outside
- F.2Above and below
- F.3Beside and next to
- F.4Left and right
- F.5Left, middle and right
- F.6Top and bottom
- F.7Top, middle and bottom
- K.1Name the shape
- K.2Circles
- K.3Squares
- K.4Triangles
- K.5Rectangles
- K.6Circles, 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

## Senior-infants skills

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

## First-class skills

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

## Second-class skills

- P.9Sort shapes into a Venn diagram
- P.10Count shapes in a Venn diagram
- R.1Name the two-dimensional shape
- R.2Select two-dimensional shapes
- R.3Count sides and vertices
- R.4Compare sides and vertices
- R.5Angles: greater than, less than or equal to a right angle
- R.6Flip, turn and slide
- R.7Identify congruent shapes
- R.8Symmetry
- S.1Name the three-dimensional shape
- S.2Select three-dimensional shapes
- S.3Count vertices, edges and faces
- S.4Compare vertices, edges and faces
- S.5Identify shapes traced from solids
- S.6Identify faces of three-dimensional shapes
- S.7Shapes of everyday objects I
- S.8Shapes of everyday objects II
- T.1Perimeter
- T.2Perimeter - word problems
- T.3Find the area of figures made of unit squares
- T.4Create figures with a given area

## Third-class skills

- N.9Sort shapes into a Venn diagram
- N.10Count shapes in a Venn diagram
- R.1Identify two-dimensional shapes
- R.2Count and compare sides and vertices
- R.3Identify three-dimensional shapes
- R.4Count vertices, edges and faces
- R.5Identify faces of three-dimensional shapes
- R.6Is it a polygon?
- R.7Angles greater than, less than or equal to a right angle
- R.8Reflection, rotation and translation
- R.9Identify congruent shapes
- R.10Symmetry
- R.11Find the area of figures made of unit squares
- R.12Create figures with a given area
- R.13Find the area of rectangles and squares
- R.14Find the missing side length of a rectangle

## Fourth-class skills

- O.1Which two-dimensional figure is being described?
- O.2Identify three-dimensional figures
- O.3Count vertices, edges and faces
- O.4Identify faces of three-dimensional figures
- O.5Which three-dimensional figure is being described?
- O.6Nets of three-dimensional figures
- O.7Is it a polygon?
- O.8Number of sides in polygons
- O.9Parallel, perpendicular and intersecting lines
- O.10Acute, right, obtuse and straight angles
- O.11Types of triangles
- O.12Identify congruent figures
- O.13Identify lines of symmetry
- O.14Rotational symmetry
- P.1Perimeter
- P.2Use perimeter to determine cost
- P.3Find the area of figures made of unit squares
- P.4Create figures with a given area
- P.5Find the area or missing side length of a rectangle
- P.6Area and perimeter: word problems

## Fifth-class skills

- W.1Is it a polygon?
- W.2Number of sides in polygons
- W.3Regular and irregular polygons
- W.4Parallel, perpendicular and intersecting lines
- W.5Types of angles
- W.6Measure angles with a protractor
- W.7Classify triangles
- W.8Classify quadrilaterals
- W.9Properties of triangles and quadrilaterals
- W.10Find the unknown angle in triangles and quadrilaterals
- W.11Parts of a circle
- X.1Lines of symmetry
- X.2Rotational symmetry
- X.3Reflection, rotation and translation
- X.4Identify congruent and similar figures
- Y.1Identify three-dimensional figures
- Y.2Count vertices, edges and faces
- Y.3Nets of three-dimensional figures
- Y.4Three-dimensional figures viewed from different perspectives
- Z.1Perimeter
- Z.2Area of squares and rectangles
- Z.3Area of triangles
- Z.4Area of compound figures
- Z.5Area between two rectangles
- Z.6Area and perimeter of figures on grids
- Z.7Area and perimeter: word problems
- Z.8Use area and perimeter to determine cost
- Z.9Volume of figures made of unit cubes
- Z.10Volume of cubes and rectangular prisms

## Sixth-class skills

- BB.1Identify and classify polygons
- BB.2Measure and classify angles
- BB.3Estimate angle measurements
- BB.4Classify triangles
- BB.5Classify quadrilaterals
- BB.6Graph triangles and quadrilaterals
- BB.7Find missing angles in triangles and quadrilaterals
- BB.8Sums of angles in polygons
- BB.9Parts of a circle
- CC.1Symmetry
- CC.2Reflection, rotation and translation
- CC.3Translations: graph the image
- CC.4Reflections: graph the image
- CC.5Rotations: graph the image
- CC.6Similar and congruent figures
- CC.7Find side lengths of similar figures
- DD.1Identify polyhedra
- DD.2Which figure is being described?
- DD.3Nets of three-dimensional figures
- DD.4Front, side and top view
- EE.1Perimeter
- EE.2Area of figures made of unit squares
- EE.3Area of squares and rectangles
- EE.4Area of triangles
- EE.5Area of compound figures
- EE.6Area and perimeter of figures on grids
- EE.7Area and perimeter: word problems
- EE.8Rectangles: relationship between perimeter and area
- EE.9Compare area and perimeter of two figures
- EE.10Circles: calculate area, circumference, radius and diameter
- EE.11Circles: word problems
- EE.12Semicircles: calculate area, perimeter, radius and diameter
- EE.13Quarter circles: calculate area, perimeter and radius
- EE.14Area of compound figures with triangles, semicircles and quarter circles
- EE.15Area between two rectangles
- EE.16Area between two triangles
- EE.17Area between two circles
- EE.18Volume of figures made of unit cubes
- EE.19Volume and surface area of cubes and rectangular prisms
- EE.20Volume and surface area of triangular prisms

## First-year 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 half lines
- 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.10Side lengths and angle measures of congruent figures
- X.11Congruence statements and corresponding parts
- X.12Side lengths and angle measures of similar figures
- X.13Similar figures and indirect measurement
- Y.1Construct the midpoint or perpendicular bisector of a segment
- Y.2Construct an angle bisector
- Y.3Construct a congruent angle
- Y.4Construct a perpendicular line
- Y.5Construct parallel lines
- Y.6Construct an equilateral triangle or regular hexagon
- Y.7Construct a square
- Z.1Pythagoras' theorem: find the length of the hypotenuse
- Z.2Pythagoras' theorem: find the missing leg length
- Z.3Pythagoras' theorem: word problems
- Z.4Converse of Pythagoras' theorem: is it a right triangle?
- AA.1Bases of three-dimensional figures
- AA.2Nets of three-dimensional figures
- AA.3Front, side and top view
- BB.1Perimeter
- BB.2Area of rectangles and parallelograms
- BB.3Area of triangles and trapeziums
- BB.4Area and perimeter: word problems
- BB.5Circles: calculate area, circumference, radius and diameter
- BB.6Circles: word problems
- BB.7Semicircles: calculate area, perimeter, radius and diameter
- BB.8Quarter circles: calculate area, perimeter and radius
- BB.9Area of compound figures with triangles, semicircles and quarter circles
- BB.10Area between two shapes
- BB.11Volume
- BB.12Surface area
- BB.13Perimeter, area and volume: changes in scale

## Second-year 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.6Interior angles of polygons
- O.7Lines, line segments and half lines
- 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.9Side lengths and angle measures of congruent figures
- P.10Congruence statements and corresponding parts
- 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.1Construct the midpoint or perpendicular bisector of a segment
- R.2Construct an angle bisector
- R.3Construct a congruent angle
- R.4Construct a perpendicular line
- R.5Construct parallel lines
- R.6Construct an equilateral triangle or regular hexagon
- R.7Construct a square
- S.1Pythagoras' theorem: find the length of the hypotenuse
- S.2Pythagoras' theorem: find the missing leg length
- S.3Pythagoras' theorem: find the perimeter
- S.4Pythagoras' theorem: word problems
- S.5Converse of Pythagoras' theorem: is it a right triangle?
- T.1Parts of three-dimensional figures
- T.2Nets of three-dimensional figures
- T.3Front, side and top view
- T.4Base plans
- T.5Similar solids
- U.1Perimeter
- U.2Area
- U.3Area between two shapes
- U.4Area and perimeter: word problems
- U.5Circles, semicircles and quarter circles
- U.6Circles: word problems
- U.7Volume of prisms and cylinders
- U.8Surface area of prisms and cylinders
- U.9Volume of cones
- U.10Surface area of cones
- U.11Volume and surface area of spheres
- U.12Volume and surface area of similar solids
- U.13Perimeter, area and volume: changes in scale
- BB.5Add polynomials to find perimeter
- BB.13Multiply polynomials to find area

## Third-year skills

- E.4Minimum and maximum area and volume
- E.6Percent error: area and volume
- F.1Perimeter
- F.2Area
- F.3Symmetry
- F.4Count lines of symmetry
- F.5Draw lines of symmetry
- F.6Transversal of parallel lines
- F.7Volume
- F.8Nets of three-dimensional figures
- F.9Surface area
- F.10Congruent triangles: SSS, SAS and ASA
- F.11Similar figures: side lengths and angle measures
- F.12Similar triangles and indirect measurement
- F.13Area and perimeter of similar figures
- F.14Area between two shapes
- F.15Similar solids
- F.16Volume and surface area of similar solids
- F.17Perimeter, area and volume: changes in scale
- F.18Identify reflections, rotations and translations
- F.19Reflections, rotations and translations: find the coordinates
- F.20Reflections, rotations and translations: graph the image
- F.21Dilations and scale factors
- F.22Pythagoras' theorem
- F.23Pythagoras' theorem: word problems
- F.24Converse of Pythagoras' theorem: is it a right triangle?
- G.1Construct the midpoint or perpendicular bisector of a segment
- G.2Construct an angle bisector
- G.3Construct a congruent angle
- G.4Construct a perpendicular line
- G.5Construct parallel lines
- G.6Construct an equilateral triangle or regular hexagon
- G.7Construct a square
- H.1Trigonometric ratios: sin, cos and tan
- H.2Trigonometric ratios: csc, sec and cot
- H.3Find trigonometric functions of special angles
- H.4Find trigonometric functions using a calculator
- H.5Inverses of trigonometric functions
- H.6Trigonometric ratios: find a side length
- H.7Trigonometric ratios: find an angle measure
- H.8Solve a right triangle
- I.2Midpoints
- I.3Distance between two points
- Z.5Add polynomials to find perimeter

## Transition year skills

- F.24Find the distance between a point and a line
- F.25Find the distance between two parallel lines
- L.5Add polynomials to find perimeter
- R.1Lines, line segments and half lines
- R.2Lengths of segments on number lines
- R.3Additive property of length
- R.4Midpoints
- R.5Congruent line segments
- R.6Perpendicular Bisector Theorem
- R.7Midpoint formula
- R.8Distance formula
- S.1Angle vocabulary
- S.2Angle measures
- S.3Identify complementary, supplementary, vertical, adjacent and congruent angles
- S.4Find measures of complementary, supplementary, vertical and adjacent angles
- S.5Angle bisectors
- T.1Identify parallel, perpendicular and skew lines and planes
- T.2Transversals: name angle pairs
- T.3Transversals of parallel lines: find angle measures
- U.1Polygon vocabulary
- U.2Perimeter
- U.3Area of triangles and quadrilaterals
- U.4Area and perimeter in the coordinate plane I
- U.5Area and perimeter in the coordinate plane II
- U.6Area and circumference of circles
- U.7Area of compound figures
- U.8Area and perimeter of similar figures
- U.9Area between two shapes
- V.1Congruence statements and corresponding parts
- V.2Solve problems involving corresponding parts
- V.3Identify congruent figures
- W.1SSS and SAS Theorems
- W.2ASA and AAS Theorems
- W.3SSS, SAS, ASA and AAS Theorems
- W.4SSS Theorem in the coordinate plane
- W.5Congruency in isosceles and equilateral triangles
- W.6Hypotenuse-Leg Theorem
- X.1Congruence transformations
- X.2Compositions of congruence transformations: graph the image
- X.3Transformations that carry a polygon onto itself
- X.4Dilations: graph the image
- X.5Dilations: find the coordinates
- X.6Dilations: scale factor and classification
- X.7Dilations and parallel lines
- Y.1Classify triangles
- Y.2Triangle Angle-Sum Theorem
- Y.3Midsegments of triangles
- Y.4Triangles and bisectors
- Y.5Identify medians, altitudes, angle bisectors and perpendicular bisectors
- Y.6Angle-side relationships in triangles
- Y.7Triangle Inequality Theorem
- Z.1Identify similar figures
- Z.2Similarity ratios
- Z.3Similarity statements
- Z.4Side lengths and angle measures in similar figures
- Z.5Similar triangles and indirect measurement
- Z.6Perimeters of similar figures
- Z.7Similarity rules for triangles
- Z.8Similar triangles and similarity transformations
- Z.9Areas of similar figures
- AA.1Pythagoras' Theorem
- AA.2Converse of Pythagoras' theorem
- AA.3Pythagoras' Inequality Theorems
- AA.4Special right triangles
- BB.1Trigonometric ratios: sin, cos and tan
- BB.2Trigonometric ratios: csc, sec and cot
- BB.3Find trigonometric functions of special angles
- BB.4Find trigonometric functions using a calculator
- BB.5Inverses of trigonometric functions
- BB.6Trigonometric ratios: find a side length
- BB.7Trigonometric ratios: find an angle measure
- BB.8Solve a right triangle
- CC.1Introduction to surface area and volume
- CC.2Surface area of prisms and cylinders
- CC.3Surface area of pyramids and cones
- CC.4Volume of prisms and cylinders
- CC.5Volume of pyramids and cones
- CC.6Surface area and volume of spheres
- CC.7Introduction to similar solids
- CC.8Surface area and volume of similar solids
- CC.9Surface area and volume review
- DD.4Minimum and maximum area and volume
- DD.6Percent error: area and volume
- FF.6Geometric probability
- II.1Construct the midpoint or perpendicular bisector of a segment
- II.2Construct an angle bisector
- II.3Construct a congruent angle
- II.4Construct a perpendicular line
- II.5Construct parallel lines
- II.6Construct an equilateral triangle or regular hexagon
- II.7Construct a square
- II.8Construct a tangent line to a circle
- II.9Construct the circumcenter or incenter of a triangle
- II.10Construct the inscribed or circumscribed circle of a triangle
- II.11Construct the centroid or orthocenter of a triangle

## Fifth-year skills

- J.8Distance in the Argand plane
- T.1Convert between radians and degrees
- T.2Radians and arc length
- T.5Coterminal angles
- T.6Reference angles
- U.1Pythagoras' Theorem and its converse
- U.2Special right triangles
- U.3Trigonometric ratios: sin, cos and tan
- U.4Trigonometric ratios: csc, sec and cot
- U.5Trigonometric ratios in similar right triangles
- U.6Find trigonometric ratios using the unit circle
- U.7Sin, cos and tan of special angles
- U.9Find trigonometric functions using a calculator
- U.10Inverses of sin, cos and tan
- U.12Solve trigonometric equations I
- U.13Solve trigonometric equations II
- U.14Trigonometric ratios: find a side length
- U.15Trigonometric ratios: find an angle measure
- U.16Solve a right triangle
- U.17Law of Sines
- U.18Law of Cosines
- U.19Solve a triangle
- U.20Area of a triangle: sine formula
- U.21Area of a triangle: Law of Sines
- W.1Complementary angle identities
- W.2Symmetry and periodicity of trigonometric functions
- X.1Midsegments of triangles
- X.2Triangles and bisectors
- X.3Identify medians, altitudes, angle bisectors and perpendicular bisectors
- X.4Angle-side relationships in triangles
- X.5Triangle Inequality Theorem
- Y.1Identify similar figures
- Y.2Similarity ratios
- Y.3Similarity statements
- Y.4Side lengths and angle measures in similar figures
- Y.5Similar triangles and indirect measurement
- Y.6Perimeters of similar figures
- Y.7Similarity rules for triangles
- Y.8Similar triangles and similarity transformations
- Y.9Similarity of circles
- Y.10Triangle Proportionality Theorem
- Y.11Areas of similar figures
- Z.1Polygon vocabulary
- Z.2Perimeter
- Z.3Area of triangles and quadrilaterals
- Z.4Area and perimeter in the coordinate plane I
- Z.5Area and perimeter in the coordinate plane II
- Z.6Area and circumference of circles
- Z.7Area of compound figures
- Z.8Area between two shapes
- Z.9Area and perimeter of similar figures
- AA.1Parts of a circle
- AA.2Central angles
- AA.3Arc measure and arc length
- AA.4Area of sectors
- AA.5Circle measurements: mixed review
- AA.6Arcs and chords
- AA.7Tangent lines
- AA.8Perimeter of polygons with an inscribed circle
- AA.9Inscribed angles
- AA.10Angles in inscribed right triangles
- AA.11Angles in inscribed quadrilaterals
- BB.1Find the centre of a circle
- BB.2Find the radius or diameter of a circle
- BB.3Write equations of circles in standard form from graphs
- BB.4Write equations of circles in standard form using properties
- BB.5Convert equations of circles from general to standard form
- BB.6Find properties of circles from equations in general form
- BB.7Graph circles
- CC.1Introduction to surface area and volume
- CC.2Surface area of prisms and cylinders
- CC.3Surface area of pyramids and cones
- CC.4Volume of prisms and cylinders
- CC.5Volume of pyramids and cones
- CC.6Surface area and volume of spheres
- CC.7Introduction to similar solids
- CC.8Surface area and volume of similar solids
- CC.9Surface area and volume review
- FF.12Geometric probability
- II.1Construct the midpoint or perpendicular bisector of a segment
- II.2Construct an angle bisector
- II.3Construct a congruent angle
- II.4Construct a perpendicular line
- II.5Construct parallel lines
- II.6Construct an equilateral triangle or regular hexagon
- II.7Construct a square
- II.8Construct a tangent line to a circle
- II.9Construct the circumcenter or incenter of a triangle
- II.10Construct the inscribed or circumscribed circle of a triangle
- II.11Construct the centroid or orthocenter of a triangle

## Sixth-year skills

- L.1Convert between radians and degrees
- L.2Radians and arc length
- L.4Coterminal and reference angles
- L.5Find trigonometric ratios using right triangles
- L.6Find trigonometric ratios using the unit circle
- L.8Inverses of trigonometric functions
- L.9Solve trigonometric equations
- L.10Trigonometric ratios: find a side length
- L.11Trigonometric ratios: find an angle measure
- L.12Solve a right triangle
- L.13Law of Sines
- L.14Law of Cosines
- L.15Solve a triangle
- L.16Area of a triangle: sine formula
- L.17Area of a triangle: Heron's formula
- N.1Complementary angle identities
- N.2Symmetry and periodicity of trigonometric functions
- O.1Find the centre of a circle
- O.2Find the radius or diameter of a circle
- O.3Write equations of circles in standard form from graphs
- O.4Write equations of circles in standard form using properties
- O.5Convert equations of circles from general to standard form
- O.6Find properties of circles from equations in general form
- O.7Graph circles
- Q.8Distance in the Argand plane