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Triangles and Quadrilaterals Exploration
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Triangles and Quadrilaterals Exploration
Solve the fire-station design puzzles. Use angle and side properties to classify each shape. Show working where needed.
Shape inspection
Tui is checking triangular braces and four-sided panels for a new fire-station training tower.
1.A triangular brace has side lengths 6 cm, 6 cm and 6 cm. Classify it by its side lengths.
2.Hemi sketches a triangle with side lengths 5 cm, 5 cm and 8 cm. What is its most specific classification by side lengths?
- Equilateral
- Isosceles
- Scalene
- Right-angled
3.A triangular panel has angles of 42° and 67°. Find the third angle and classify the triangle by its angles.
4.A four-sided sign has angles 90°, 90°, 90° and 90°. What must its opposite sides be like, and what family of quadrilaterals does it belong to?
5.Hugo checks a panel with four equal sides but no right angles. Which shape is it?
- Rectangle
- Rhombus
- Trapezium
- Kite
6.True or false: Every square is a rectangle because it has four right angles and two pairs of opposite sides parallel.
TrueFalse
Design calculations
The team is choosing shapes that will fit together safely. Use the given measurements and explain your decisions.
7.A quadrilateral’s interior angles are 105°, 80°, 95° and x°. Calculate x. (The interior angles of any quadrilateral total 360°.)
8.A rectangular equipment panel is 1.8 m long and 1.2 m wide. Calculate its perimeter and area.
9.The crew wants a quadrilateral brace with exactly one pair of parallel sides. What is this shape called in New Zealand geometry vocabulary?
10.Tui says, “A quadrilateral with four equal sides must be a square.” Is she correct? Explain how you can tell a square from another quadrilateral with four equal sides.
11.The team needs a triangular brace with side lengths 4 cm, 7 cm and 12 cm. Can these lengths form a triangle? State the rule you used.
12.For a final design, draw a quadrilateral that has exactly one pair of parallel sides. Label the parallel sides and write its name.
2 printable pages
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