# 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!

## Senior-infants skills

- I.1Inside and outside
- I.2Left, middle and right
- I.3Top, middle and bottom
- I.4Above and below
- I.5Location in a grid
- M.9Count shapes in a Venn diagram
- R.1Identify shapes I
- R.2Identify shapes II
- R.3Identify solid figures
- R.4Relate planar and solid figures
- R.5Count sides and corners
- R.6Compare sides and corners
- R.7Geometry of everyday objects
- R.8Symmetry I
- R.9Symmetry II

## First-class skills

- I.1Identify 2-dimensional shapes
- I.2Identify 3-dimensional figures
- I.3Geometry of everyday objects
- I.4Relate planar and solid figures
- I.5Count sides and vertices
- I.6Count edges, vertices and faces
- I.7Compare sides and vertices
- I.8Compare edges, vertices and faces
- I.9Open and closed shapes
- I.10Flip, turn and slide
- I.11Symmetry
- I.12Same shape
- J.1Left, middle and right
- J.2Above, below, top, middle and bottom
- J.3Location in a grid
- P.2Count shapes in a Venn diagram

## Second-class skills

- P.9Sort shapes into a Venn diagram
- P.10Count shapes in a Venn diagram
- Q.1Identify 2-dimensional and 3-dimensional shapes
- Q.2Count sides and angles
- Q.3Count edges, vertices and faces
- Q.4Compare sides and angles
- Q.5Compare edges, vertices and faces
- Q.6Symmetry
- Q.7Congruent
- Q.8Flip, turn and slide
- Q.9Area
- Q.10Create figures with a given area
- Q.11Angles: greater than, less than or equal to a right angle

## Third-class skills

- N.9Sort shapes into a Venn diagram
- N.10Count shapes in a Venn diagram
- R.1Identify 2-dimensional and 3-dimensional shapes
- R.2Count and compare sides and angles
- R.3Count and compare edges, vertices and faces
- R.4Symmetry
- R.5Similar and congruent
- R.6Reflection, rotation and translation
- R.7Area
- R.8Create figures with a given area
- R.9Angles: greater than, less than or equal to a right angle
- R.10Is it a polygon?

## Fourth-class skills

- L.1Identify planar and solid figures
- L.2Types of triangles
- L.3Open and closed shapes and qualities of polygons
- L.4Which 2-dimensional shape is being described?
- L.5Which 3-dimensional figure is being described?
- L.6Number of sides in polygons
- L.7Count and compare sides, edges, faces and vertices
- L.8Similar and congruent
- L.9Nets of 3-dimensional figures
- L.10Acute, right, obtuse and straight angles
- L.11Perimeter
- L.12Area of figures made of unit squares
- L.13Create figures with a given area
- L.14Use perimeter to determine cost
- L.15Lines of symmetry
- L.16Rotational symmetry
- L.17Parallel, perpendicular, intersecting

## Fifth-class skills

- V.1Identify planar and solid figures
- V.2Types of triangles
- V.3Open and closed shapes and qualities of polygons
- V.4Regular and irregular polygons
- V.5Number of sides in polygons
- V.6Which figure is being described?
- V.7Classify quadrilaterals
- V.8Reflection, rotation and translation
- V.9Count and compare sides, edges, faces and vertices
- V.10Similar and congruent
- V.11Nets of 3-dimensional figures
- V.12Types of angles
- V.13Measure angles with a protractor
- V.14Parts of a circle
- V.15Perimeter
- V.16Area of squares and rectangles
- V.17Area of triangles
- V.18Area of compound figures
- V.19Area between two rectangles
- V.20Area and perimeter of figures on grids
- V.21Area and perimeter: word problems
- V.22Use area and perimeter to determine cost
- V.23Volume of figures made of unit cubes
- V.24Volume of cubes and rectangular prisms
- V.25Three-dimensional figures viewed from different perspectives
- V.26Lines of symmetry
- V.27Rotational symmetry
- V.28Parallel, perpendicular, intersecting
- V.29Find the unknown angle in triangles and quadrilaterals

## Sixth-class skills

- AA.1Review of 2- and 3-dimensional figures
- AA.2Angle review: measure and classify
- AA.3Estimate angle measurements
- AA.4Triangle review
- AA.5Classify quadrilaterals
- AA.6Find missing angles and side lengths in triangles and quadrilaterals
- AA.7Sums of angles in polygons
- AA.8Parts of a circle
- AA.9Similar and congruent figures
- AA.10Find side lengths of similar figures
- AA.11Reflection, rotation and translation
- AA.12Translations: graph the image
- AA.13Reflections: graph the image
- AA.14Rotations: graph the image
- AA.15Symmetry
- AA.16Perimeter
- AA.17Area of figures made of unit squares
- AA.18Area of squares and rectangles
- AA.19Area of triangles
- AA.20Area of compound figures
- AA.21Area and perimeter of figures on grids
- AA.22Area and perimeter: word problems
- AA.23Rectangles: relationship between perimeter and area
- AA.24Compare area and perimeter of two figures
- AA.25Circles: calculate area, circumference, radius and diameter
- AA.26Circles: word problems
- AA.27Identify polyhedra and count faces, edges and vertices
- AA.28Which figure is being described?
- AA.29Front, side and top view
- AA.30Nets of 3-dimensional figures
- AA.31Volume of figures made of unit cubes
- AA.32Volume and surface area of cubes and rectangular prisms
- AA.33Volume and surface area of triangular prisms
- AA.34Semicircles: calculate area, perimeter, radius and diameter
- AA.35Quarter circles: calculate area, perimeter and radius
- AA.36Area of compound figures with triangles, semicircles and quarter circles
- AA.37Area between two rectangles
- AA.38Area between two triangles
- AA.39Area between two circles

## First-year skills

- X.1Lines, line segments and half lines
- X.2Parallel, perpendicular, intersecting
- X.3Name, measure and classify angles
- X.4Identify complementary, supplementary, vertical, adjacent and congruent angles
- X.5Find measures of complementary, supplementary, vertical and adjacent angles
- X.6Transversal of parallel lines
- X.7Classify triangles
- X.8Classify quadrilaterals
- X.9Find missing angles in triangles and quadrilaterals
- X.10Identify and classify polygons
- X.11Interior angles of polygons
- X.12Similar and congruent figures
- X.13Similar figures: side lengths and angle measures
- X.14Similar figures and indirect measurement
- X.15Congruent figures: side lengths and angle measures
- X.16Congruence statements and corresponding parts
- X.17Perimeter
- X.18Area of rectangles and parallelograms
- X.19Area of triangles and trapeziums
- X.20Area and perimeter: word problems
- X.21Parts of a circle
- X.22Circles: calculate area, circumference, radius and diameter
- X.23Circles: word problems
- X.24Find lengths and measures of bisected lines and angles
- X.25Front, side and top view
- X.26Names and bases of 3-dimensional figures
- X.27Nets of 3-dimensional figures
- X.28Surface area
- X.29Volume
- X.30Perimeter, area and volume: changes in scale
- X.31Semicircles: calculate area, perimeter, radius and diameter
- X.32Quarter circles: calculate area, perimeter and radius
- X.33Area of compound figures with triangles, semicircles and quarter circles
- X.34Area between two shapes
- Y.1Identify reflections, rotations and translations
- Y.2Translations: graph the image
- Y.3Translations: find the coordinates
- Y.4Reflections: graph the image
- Y.5Reflections: find the coordinates
- Y.6Rotations: graph the image
- Y.7Rotations: find the coordinates
- Y.8Symmetry
- Z.1Construct the midpoint or perpendicular bisector of a segment
- Z.2Construct an angle bisector
- Z.3Construct a congruent angle
- Z.4Construct a perpendicular line
- Z.5Construct parallel lines
- Z.6Construct an equilateral triangle or regular hexagon
- Z.7Construct a square
- AA.1Pythagoras' theorem: find the length of the hypotenuse
- AA.2Pythagoras' theorem: find the missing leg length
- AA.3Pythagoras' theorem: word problems
- AA.4Converse of Pythagoras' theorem: is it a right triangle?

## Second-year skills

- N.1Lines, line segments and half lines
- N.2Identify complementary, supplementary, vertical, adjacent and congruent angles
- N.3Find measures of complementary, supplementary, vertical and adjacent angles
- N.4Transversal of parallel lines
- N.5Classify triangles
- N.6Classify quadrilaterals
- N.7Find missing angles in triangles and quadrilaterals
- N.8Identify and classify polygons
- N.9Interior angles of polygons
- N.10Similar and congruent figures
- N.11Similar figures: side lengths and angle measures
- N.12Congruent figures: side lengths and angle measures
- N.13Congruence statements and corresponding parts
- N.14Congruent triangles: SSS, SAS and ASA
- N.15Perimeter
- N.16Area
- N.17Area between two shapes
- N.18Area and perimeter: word problems
- N.19Parts of a circle
- N.20Circles, semicircles and quarter circles
- N.21Circles: word problems
- N.22Find lengths and measures of bisected lines and angles
- N.23Front, side and top view
- N.24Base plans
- N.25Names and parts of 3-dimensional figures
- N.26Nets of 3-dimensional figures
- N.27Surface area of prisms and cylinders
- N.28Surface area of cones
- N.29Volume of prisms and cylinders
- N.30Volume of cones
- N.31Volume and surface area of spheres
- N.32Similar solids
- N.33Volume and surface area of similar solids
- N.34Perimeter, area and volume: changes in scale
- O.1Pythagoras' theorem: find the length of the hypotenuse
- O.2Pythagoras' theorem: find the missing leg length
- O.3Pythagoras' theorem: find the perimeter
- O.4Pythagoras' theorem: word problems
- O.5Converse of Pythagoras' theorem: is it a right triangle?
- P.4Distance between two points
- Q.1Identify reflections, rotations and translations
- Q.2Translations: graph the image
- Q.3Translations: find the coordinates
- Q.4Reflections: graph the image
- Q.5Reflections: find the coordinates
- Q.6Rotations: graph the image
- Q.7Rotations: find the coordinates
- Q.8Dilations: graph the image
- Q.9Dilations: find the coordinates
- Q.10Dilations: scale factor and classification
- Q.11Symmetry
- 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
- Z.5Add polynomials to find perimeter
- Z.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 3-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.20Find the distance between a point and a line
- F.21Find 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 angles
- 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 angles
- 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