# Making triangles

Students study the concept of triangle inequality, which determines if three positive numbers can serve as the side lengths of a triangle. This principle states that a triangle is possible if the largest of the three numbers is smaller than the sum of the other two. To explore this, students experiment with various combinations of three natural numbers. They investigate whether these numbers can form a triangle and, when they do, students classify and construct the corresponding triangle. Additionally, they learn to calculate the perimeter of these triangles.

This lesson also reviews content from Year 7 to enable students to successfully engage in four related lessons that explore the Year 8 Pythagoras theorem content.

Year level(s) Year 7, Year 8
Audience Teacher
Purpose Teaching resource
Format Web page
Teaching strategies and pedagogical approaches Mathematics investigation, Questioning, Explicit teaching, Concrete Representational Abstract model
Keywords triangles, congruence, similarity, algorithms, Maths Hub lesson plan

## Curriculum alignment

Curriculum connections Critical and creative thinking
Strand and focus Measurement, Space
Topics Shapes and objects, Area, volume and surface area, Computational thinking
AC: Mathematics (V9.0) content descriptions
AC9M7SP02
Classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships

AC9M8M01
Solve problems involving the area and perimeter of irregular and composite shapes using appropriate units

AC9M8SP01
Identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations

AC9M8SP04
Design, create and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works

Numeracy progression Understanding geometric properties (P4, P7)
Understanding units of measurement (P8)
Proportional thinking (P6)