Measurement – Geometric Figures: Triangles

Strategy

Students can:

  • identify the elements preserved in similar triangles
  • determine whether triangles are similar
  • apply the enlargement or reduction factor to find unknown sides in similar triangles
  • calculate the length of unknown sides in pairs of similar triangles

Activities to support the strategy

Activity 1

1. Discuss as a class the definition of similar figures and ask students to copy the following.

Two figures are similar if they have exactly the same shape when enlarged or reduced. Figures can be enlarged or reduced, translated, reflected and/or rotated and still be similar figures.

2. Have students investigate similar figures using GeoGebra resources found in the Geometers Warehouse

3. In pairs, ask students to complete the measurements for two similar triangles and another two similar triangles.

View/print (PDF 121.86KB)

View/print (PDF 124.64KB)

Ask pairs of students to share their answers with another pair of students, discuss any differences and determine the group's comments when comparing the similar triangles.

Ask groups of four to share with another four students, discuss any differences and determine the group's comments when comparing the similar triangles.

As a class, discuss the two similar triangles:

  • What did you notice about the angles A and X?
  • What did you notice about the angles B and Y?
  • What did you notice about the angles C and Z?
  • What did you notice about AB : XY?
  • What did you notice about BC : YZ?
  • What did you notice about CA : ZX?

Ask students to copy the following.

  • When two figures are similar, they have:
  • one pair of angles measuring the same number of degrees
  • another pair of angles measuring the same number of degrees
  • the third pair of angles measuring the same number of degrees
  • the ratio of the side lengths is always the same

4. Hand out the worksheet Similar triangles and ask students in small groups to investigate one collection of triangles and report their findings back to the class.

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5. Ask students in small groups to complete the worksheet Scale factor.

View/print (PDF 342.57KB)

6. As a class, discuss which of the triangles are similar and how this was decided.

References

Australian curriculum

ACMMG165: Classify triangles according to their side and angle properties and describe quadrilaterals

NSW syllabus

MA4-17MG: Classifies, describes and uses the properties of triangles and quadrilaterals and determines congruent triangles to find unknown side lengths and angles

Teacher resources

Math open reference: The user can drag any vertex of two similar triangles and notice the triangles change shape but still remain similar. Also includes similar triangles with shared parts.

Cut the knot: Investigating side lengths and angles

Cut the knot: An interesting extension to work on similar triangles

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