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Geometry Problem Solving Workshop
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Geometry Problem Solving Workshop
Solve each problem and show your reasoning. Include units where appropriate, and name the geometric rule you use.
Angle reasoning
Use angle facts to find unknowns and explain how you know.
1.At a road junction, two straight roads cross. One angle is 128°. What is the size of the angle directly opposite it? Choose the correct answer.
- 52°
- 62°
- 128°
- 232°
2.A triangular shade sail has two interior angles of 47° and 68°. Calculate the third interior angle.
3.A window frame has two parallel horizontal bars crossed by a diagonal support. The acute angle where the support meets the lower bar is 54°. What is the size of the alternate interior angle where it meets the upper bar? State the angle rule.
4.The diagram shows a 128° angle. The adjacent angle lies on the same straight line. Find the adjacent angle and explain the rule you used.
Shapes, measures and reasoning
Apply geometric properties to practical designs. Show the steps behind your answers.
5.A rectangular garden has a perimeter of 34 m and a width of 6 m. Find its length. Show how the perimeter formula leads to your answer.
6.A regular hexagonal sign has a perimeter of 42 cm. Calculate the length of one side, then state how many triangles are formed when the centre is joined to every vertex.
7.A student says, “Every rectangle is a square because both shapes have four right angles.” Is the reasoning correct? Explain what additional condition a rectangle must meet to be a square, and give a counterexample.
8.A right-angled triangular brace has perpendicular sides of 9 cm and 12 cm. Use Pythagoras’ theorem to find the length of the longest side.
9.A circular garden has a radius of 4 m. Calculate its area using π ≈ 3.14. Give your answer to 1 decimal place and include units.
10.A designer needs a triangle with side lengths 5 cm, 7 cm and 13 cm. Can these lengths make a triangle? Justify your decision using a rule about side lengths.
TrueFalse
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