Reason with geometric theorems
Practise online with Next and Previous buttons, worked explanations and a report of the questions to review.
Log in to continueUse a chain of stated reasons to solve spatial problems and develop proofs.
One-question preview
Choose one answer
Try this sample, or continue to the online quiz for a practice set with Next and Previous buttons.
An isosceles triangle has equal sides AB and AC. Its base angle at B is 30°. Find the angle at A.
Show worked steps
Answer: 120°
- Angles opposite equal sides are equal, so angle C equals angle B.
- The triangle angle sum gives A = 180° − 2×30°.
- A = 120°.
- 2 × 30 = 60.
- 180 − 60 = 120.
This is a question from this topic’s quiz. Preview answers are not saved.
Scratchpad
Working out
Draw with a finger, pen or mouse, or type your working below.
Your working stays on this page. It is not submitted or saved, and clears when you leave or reload.
Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Use a chain of stated reasons to solve spatial problems and develop proofs.
Read the official VCAA curriculum description (VC2M10SP01)
These quizzes practise concepts within this topic. Multiple-choice answers alone do not demonstrate drawing, conducting an investigation or using a digital tool.
Activities to practise beyond the quiz
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M10SP01-C01Use equal sides, equal angles and angle sums.
- VC2M10SP01-C02Formulate a deductive geometric proof.
- VC2M10SP01-C03Use parallel-line theorems to justify a conclusion.
- VC2M10SP01-C04Develop and communicate a plane-shape proof rather than only selecting an answer.
- VC2M10SP01-C05Apply and explain reason with geometric theorems using calculate and explain each step.
- VC2M10SP01-C06Apply and explain reason with geometric theorems using compare evidence and check a claim.
Learn with worked examples
Help with this topic
Skills in this topic
Traceable coverage
Subskills
These practice subskills map to the curriculum topic. Guided activities cover skills beyond multiple-choice questions.
Descriptor-derived subskills
- D01Justify each stepUse equal sides, equal angles and angle sums.
- D02Connect several angle factsUse parallel-line theorems to justify a conclusion.
- D03Calculate and explain each stepApply and explain reason with geometric theorems using calculate and explain each step.
- D04Compare evidence and check a claimApply and explain reason with geometric theorems using compare evidence and check a claim.