1
WORK PROGRAM
Chapter 13 Congruence and similarity
Strand:Space and geometry; Measurement
Substrands and outcomes:
Two-dimensional spaceSGS3.2a Manipulates, classifies and draws two-dimensional shapes and describes side and angle properties
Two-dimensional spaceSGS3.2b Measures, constructs and classifies angles
PositionSGS3.3 Uses a variety of mapping skills
Properties of geometrical figuresSGS4.3 Classifies, constructs and determines the properties of triangles and quadrilaterals
Properties of geometrical figuresSGS4.4 Identifies congruent and similar two-dimensional figures stating the relevant conditions
LengthMS2.1 Estimates, measure, compares and records lengths, distances and perimeters in metres, centimetres and millimetres
AreaMS3.2 Selects and uses the appropriate unit to calculate area, including the area of squares, rectangles and triangles
Perimeter and areaMS4.1 Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and figures composed of rectangles and triangles
Section / GC tips, Investigations, History of mathematics, Maths Quest challenge,10 Quick Questions,
Code puzzles / SkillSHEETs, WorkSHEETs, Interactive games, Test yourself, Topic tests
(CD–ROM) / Technology applications
(CD–ROM) /
Learning outcomes
Are you ready? (page480) / SkillSHEETs (page 480)13.4: Reflection of an object
13.6: Rotation of an object through 180
13.7: Measuring and drawing lines
13.9: Ruler and protractor skills
13.10: Converting units of length / MS2.1
- recording lengths or distances using centimetres and millimetres
- converting between metric units of length
- identifying congruent figures by superimposing them through a combination of rotations, reflections and translations
Transformations (page481)
Translations (page481)
WE 1, 2, 3
Ex 13A Translations (page484) / Maths Quest challenge: Q1-2 (page 485) / SkillSHEET 13.1: Moving up and down or left and right (page484)
SkillSHEET 13.2: Translation of a point (page484)
Game time 001 (page485) / Cabri geometry: Translation (page 484)
Mathcad: Translations (page 484) / SGS4.4
- identifying congruent figures by superimposing them through a combination of rotations, reflections and translations
- using dynamic geometry software to investigate the properties of geometric figures (Applying strategies, Reasoning)
Reflections (page 486)
WE 4a-b, 5a-b
Ex 13B Reflections (page489) / 10 Quick Questions 1 (page 491) / SkillSHEET 13.3: Reflection of a point (page489)
SkillSHEET 13.4: Reflection of an object (page489)
WorkSHEET 13.1 (page490) / Cabri geometry: Reflection (page 489) / SGS4.4
- identifying congruent figures by superimposing them through a combination of rotations, reflections and translations
- using dynamic geometry software to investigate the properties of geometric figures (Applying strategies, Reasoning)
Rotations (page 492)
WE 6, 7a-b, 8
Ex 13C Rotations (page495) / Investigation: In a spin (page 493)
Investigation: Designing a patchwork quilt (page498) / SkillSHEET 13.5: Rotation of a point (page495)
SkillSHEET 13.6: Rotation of an object through 180 (page495)
Game time 002 (page 497) / Cabri geometry: Rotation (page 494)
Cabri geometry: Rotation (page 495)
Cabri geometry: Transformations (page498) / SGS3.2b
- identifying the arms and vertex of an angle where both arms are invisible, such as rotations and rebounds
- identifying congruent figures by superimposing them through a combination of rotations, reflections and translations
- using dynamic geometry software to investigate the properties of geometric figures (Applying strategies, Reasoning)
- recognising congruent figures in design work (Reflecting)
Constructing congruent triangles (page 499)
WE 9, 10, 11
Ex 13D Constructing congruent triangles (page 501) / 10 Quick Questions 2 (page 502) / SkillSHEET 13.7: Measuring and drawing lines (page501)
SkillSHEET 13.8: Constructing angles with a protractor (page501) / Cabri geometry: Three sides (page 501)
Cabri geometry: Two angles and a side (page501)
Cabri geometry: Two sides and an angle between (page 501) / SGS3.2a
- using templates, rulers, set squares and protractors to draw regular and irregular two-dimensional shapes
- using a protractor to construct an angle of a given size and to measure angles
- constructing various types of triangles using geometrical instruments, given different information
- drawing congruent figures using geometric instruments
- using dynamic geometry software to investigate the properties of geometric figures (Applying strategies, Reasoning)
Congruent figures (page503)
WE 12, 13
Ex 13E Congruent figures (page 504) / Code puzzle (page 506) / WorkSHEET 13.2 (page505) / SGS4.3
- labelling and naming triangles and quadrilaterals in text and on diagrams
- matching sides and angles of two congruent polygons
- naming the vertices in matching order when using the symbol in a congruence statement
- applying geometrical facts, properties and relationships to solve problems such as finding unknown sides and angles in diagrams (Applying strategies, Reasoning)
Dilations (page 507)
WE 14, 15, 16
Ex 13F Dilations (page509) / Investigation: Braille (page 511) / SkillSHEET 13.9: Ruler and protractor skills (page509) / Cabri geometry: Dilation (page 509) / SGS3.2a
- making enlargements and reductions of two-dimensional shapes, pictures and maps
- comparing and discussing representations of the same object or scene in different sizes
- enlarging or reducing a graphic using computer software (Applying strategies)
- using the term ‘similar’ for any two figures that have the same shape but not necessarily the same size
- determining that shape, angle size and the ratio of matching sides are preserved in similar figures
- determining the scale factor for a pair of similar polygons
- determining the scale factor for a pair of circles
- drawing similar figures using geometrical instruments
- using dynamic geometry software to investigate the properties of geometric figures (Applying strategies, Reasoning)
Similar figures (page 512)
WE 17
Ex 13G Similar figures (page 513) / SGS3.2a
- comparing and discussing representations of the same object or scene in different sizes
- using the term ‘similar’ for any two figures that have the same shape but not necessarily the same size
- matching the sides and angles of similar figures
- naming the vertices in matching order when using the symbol in a similarity statement
- calculating dimensions of similar figures using the enlargement or reduction factor
- applying similarity to finding lengths in the environment where it is impractical to measure directly (Applying strategies, Reasoning)
- applying geometrical facts, properties and relationships to solve problems such as finding unknown sides and angles in diagrams (Applying strategies, Reasoning)
Scale drawing (page 515)
WE 18, 19, 20
Ex 13H Scale drawing (page 517) / SkillSHEET 13.10: Converting units of length (page517)
WorkSHEET 13.3 (page519) / Mathcad: Ratio scales (page 517)
Excel: Map scales (page517)
Excel: Map scales (DIY (page 517) / SGS3.2a
- making enlargements and reductions of two-dimensional shapes, pictures and maps
- comparing and discussing representations of the same object or scene in different sizes
- recognising that the same location can be represented by maps or plans using different scales
- using scale to calculate the distance between two points on a map
- interpreting scales on maps and plans (Applying strategies, Reflecting)
- calculating dimensions of similar figures using the enlargement or reduction factor
- choosing an appropriate scale in order to enlarge or reduce a diagram
- constructing scale drawings
- drawing similar figures using geometrical instruments
- reading and interpreting scales on maps and simple scale drawings to calculate area
Summary (page 520)
Chapter review (page 521) / ‘Test yourself’ multiple choice questions
(page 522)
Topic tests (2)