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Geometry Problem Solving Workshop
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Geometry Problem Solving Workshop
Solve each challenge and show enough working to make your reasoning clear. Give units where needed. Diagrams are not necessarily drawn to scale.
Angle investigations
Use angle facts to help plan a new lookout platform on the coast.
1.A triangular support has two angles of 38° and 67°. Calculate the third angle and state the angle fact you used.
2.The lookout platform is a parallelogram. One interior angle is 112°. Find the other three interior angles.
3.A regular hexagonal window is fitted into the lookout. What is the size of each interior angle?
- 120°
- 125°
- 135°
- 140°
4.A quadrilateral support frame has interior angles x°, 2x°, 3x° and 4x°. Find x and all four angles. Could the frame be a rectangle? Explain briefly.
Scale, area and shape
Use measurement and geometry to make the lookout practical.
5.A rectangular viewing deck measures 9 m by 6 m. A 1 m-wide path is built all the way around the outside. Calculate the area of the path alone.
6.A scale model of a triangular roof uses a scale of 1:40. The model’s roof edge is 18 cm long. How long is the matching edge on the real roof, in metres?
7.Two similar triangular braces have corresponding side lengths in the ratio small:large = 3:5. The small brace has perimeter 27 cm. Find the large brace’s perimeter and explain why the same scale factor applies.
8.A triangular roof panel has sides 7 m and 10 m with an included angle of 60°. Use the cosine rule to calculate the third side, to 2 decimal places.
9.A designer says, “Every rectangle is a square.” Is this statement true or false? Give a counterexample or explanation.
TrueFalse
10.A regular polygon has an exterior angle of 30°. How many sides does it have, and what is each interior angle?
11.A triangular brace has side lengths 5 m, 6 m and 9 m. Explain how you can tell whether it is right-angled without measuring its angles.
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