# 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 three-by-three grid
- 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 three-by-three grid

## 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.13Use perimeter to determine cost
- L.14Lines of symmetry
- L.15Rotational symmetry
- L.16Parallel, perpendicular, intersecting

## Fifth-class skills

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

## Sixth-class skills

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

## First-year skills

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

## Second-year skills

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

- 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.4Congruency in isosceles and equilateral triangles
- W.5Hypotenuse-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.3Pythagorean 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

## 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

## Sixth-year skills

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