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WORK PROGRAM
Chapter 9 Congruence and similarity
Strands: Space and geometry, Measurement
Substrandsandoutcomes:
Properties of geometrical figuresSGS4.4 Identifies congruent and similar two-dimensional figures stating the relevant conditions
Properties of geometrical figuresSGS5.2.2 Develops and applies results for proving that triangles are congruent or similar
Deductive geometrySGS5.3.1 Constructs arguments to prove geometrical results
Deductive geometrySGS5.3.3 Constructs geometrical arguments using similarity tests for triangles
Surface area and volumeMS5.3.1 Applies formulae to find the surface area of pyramids, right cones and spheres
Section / GC tips, Investigations,History of mathematics, Maths Quest challenge, 10 Quick Questions,
Code puzzles,
Career profiles / SkillSHEETs, WorkSHEETs, Interactive games, Testyourself, Topic tests
(CD-ROM) / Technology applications
(CD-ROM) / Learning outcomes
Are you ready? (page 318) / SkillSHEETs (page 318)
9.1: Corresponding sides and angles of congruent triangles
9.2: Finding the scale factor
9.4: Translation of a point
9.5: Rotation of a point
9.6: Reflection of a point / SGS4.4
- identifying congruent figures by superimposing them through a combination of rotations, reflections and translations
- matching sides and angles of two congruent polygons
- determining the scale factor for a pair of similar polygons
Congruent figures (page319)
WE 1a–d, 2, 3, 4
Ex 9A Congruent figures (page 322) / SkillSHEET 9.1: Corresponding sides and angles of congruent triangles (page 322)
Game time 001 (page325) / SGS5.2.2
- determining what information is needed to show that two triangles are congruent
- applying the congruency tests to justify that two triangles are congruent
- applying the four triangle congruency tests in numerical exercises to find unknown sides and angles
- applying the properties of congruent and similar triangles to solve problems, justifying the results (Applying strategies, Reasoning)
- determining minimum conditions to deduce two triangles are congruent
- writing formal proofs of congruence of triangles, preserving matching order of vertices
Similar figures (page 326)
WE 5, 6a–c, 7, 8
Ex 9B Similar figures (page 330) / Investigation: Map measurements (page 335)
Maths Quest challenge: Q1–2 (page 335)
History of mathematics: Thales of Miletus (page336)
Investigation: Midpoints and similar triangles (page 336)
Code puzzle (page 337)
10 Quick Questions 1 (page 338) / SkillSHEET 9.2: Finding the scale factor (page331)
SkillSHEET 9.3: Calculating unknown sides in a pair of similar triangles (page 331)
Game time 002 (page334)
WorkSHEET 9.1 (page334) / Cabri geometry: Similar triangles (page 326)
Cabri geometry: Similar triangles (page 330)
Mathcad: Similarity (page332)
Cabri geometry: Shortest distance (page 335)
Cabri geometry: Triangle midpoints (page 336)
Cabri geometry: Quadrilateral midpoints (page 336) / SGS5.2.2
- identifying the elements preserved in similar triangles, namely angle size and the ratio of corresponding sides
- determining whether triangles are similar
- applying the enlargement or reduction factor to find unknown sides in triangles
- calculating unknown sides in a pair of similar triangles
- determining what information is needed to establish that two triangles are similar
- writing formal proofs of similarity of triangles in the standard four- or five-line format, preserving the matching order of vertices, identifying the similarity factor when appropriate, and drawing relevant conclusions from this similarity
- proving and applying further theorems using similarity
- proving statements about geometrical figures (Reasoning, Communication, Applying strategies)
- solving problems using deductive reasoning (Reasoning, Applying strategies)
- establishing and applying the fact that in two similar figures with similarity ratio 1: k, matching areas are in the ratio 1: k2
- solving problems involving the similarity ratio and areas (Applying strategies)
Area and volume of similar figures (page339)
WE 9a–b
Ex 9C Area and volume of similar figures (page341) / Investigation: Investigating the area and volume of similar figures (page 339)
10 Quick Questions 2 (page 342) / WorkSHEET 9.2 (page342) / MS5.3.1
- establishing and applying the fact that in two similar figures with similarity ratio 1: k matching angles have the same size, matching intervals are in the ratio 1: k, matching areas are in the ratio 1: k2, matching volumes are in the ratio 1: k3
- solving problems involving the similarity ratio and areas and volumes (Applying strategies)
Transformation of points and figures (page 343)
WE 10a–b, 11a–c, 12, 13a–b, 14a–d, 15, 16a–d
Ex 9D Transformation of points and figures (page352) / Investigation: Using a mira (page 348) / SkillSHEET 9.4: Translation of a point (page 352)
SkillSHEET 9.5: Rotation of a point (page 352)
SkillSHEET 9.6: Reflection of a point (page 353)
WorkSHEET 9.3 (page355) / SGS4.4
- identify congruent figures by superimposing them through a combination of rotations, reflections and translations
- drawing congruent figures using geometrical instruments
- calculating dimensions of similar figures using enlargement or reduction factor
- constructing scale drawings
- drawing similar figures using geometrical instruments
- applying the enlargement or reduction factor to find unknown sides in similar triangles
- applying properties of congruent and similar triangles to solve problems, justifying the results (Applying strategies, Reasoning)
- applying simple deductive reasoning in solving numerical and non-numerical problems (Applying strategies, Reasoning)
Summary (page 356)
Chapter review (page 357) / ‘Test yourself’ multiple choice questions (page360)
Topic tests (2)