Stage 4 - angles – find missing angles

Strategy

Students can:

  • Recognise and isosceles, equilateral and scalene triangle and identify the specific angle properties related to each type
  • Use the angle sum of a triangle property to find the missing angles in a triangle

Activities to support the strategy

Students need to use their understanding of the angle properties of isosceles, equilateral and scalene triangles and the angle sum of a triangle to find the missing angles in a triangle. Students will first need to be confident in using the appropriate symbols and notations when indicating equal sides and equal angles in geometrical figure. Activities should also extend to include examples of quadrilaterals and other simple figures.

Activity 1

Students should first review their understanding of geometric notation. A number of questions demonstrating all three types of triangles should be shown using both numbers and generalised symbols should be provided.

The same number of ‘notches’ indicates equal sides
The same symbol indicates equal angles

Students should then practice a number of examples which focus on finding the size of the missing angle. Students should be encouraged to mark missing values on their diagrams and to show their calculations. A variety of examples should be demonstrated. It is also an opportunity to explore deductive geometrical reasoning.

Since the triangle is marked as isosceles, the missing base angle is 75°.
The angle sum of a triangle is 180°,
∴  x + 75 + 75 = 18
x = 180 – 150
x = 30

The triangle is marked to indicate that it is an equilateral triangle, with all three angles being equal
3x = 180
x =

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Students should then practice these skills and techniques.

Activity 2

Students can investigate the fundamental properties of triangles and other figures using GeoGebra resources found in the Geometers Warehouse

References

Australian curriculum

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

NSW syllabus

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

Student resources

Exploring triangles

Scootle - Find an active triangle in a photograph. Work out its angles by applying principles of opposite angles, complementary angles, supplementary angles and the sum of interior angles. Watch a video showing how triangles are used in buildings and other structures.

Geometric reasoning including parallel lines and angle sum of a triangle

Supporting Australian Mathematics Project -This is a website designed for both teachers and students that addresses geometry from the Australian Curriculum. It contains material on geometry and includes information regarding parallel lines and the angle sum of triangles. There are pages for both teachers and students. The student pages contain interactive questions for students to check their progress in the topic.

Maths is Fun

Students can use the Maths is Fun online activity to verify the angle sum of a triangle property.

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