Topic Review — Triangles & Quadrilaterals

Review Questions

1. Classify each triangle: Fluency

   1. A triangle with sides 5 cm, 5 cm, and 5 cm
   2. A triangle with angles 90°, 45°, and 45° — classify by both angle and side
   3. A triangle with sides 3 cm, 4 cm, and 7 cm and all different angles
   4. A triangle with angles 110°, 35°, and 35° — classify by both angle and side

2. Classify each quadrilateral: Fluency

   1. 2 pairs of parallel sides, 4 equal sides, no right angles
   2. Exactly 1 pair of parallel sides
   3. 2 pairs of equal adjacent sides
   4. True or False: every square is a rectangle.

3. Find the missing angle: Fluency

   1. A triangle with angles 55° and 70°
   2. An isosceles triangle with two angles of 40°
   3. A quadrilateral with angles 90°, 120°, and 85°
   4. What is the size of each angle in an equilateral triangle?
   5. A quadrilateral with angles 80°, 100°, and 95°

4. Calculate the area of each shape: Understanding

   1. A rectangle 12 cm × 7 cm
   2. A square with side length 9 cm
   3. A rectangle with area 96 cm² and length 16 cm — find the width
   4. A path 25 m × 3.5 m

5. A rectangular garden measures 15 m × 8 m. Problem Solving

   1. What is the area of the garden?
   2. A path 1 m wide is built around the outside of the garden. What are the outer dimensions?
   3. What is the area of just the path?

6. Properties of quadrilaterals: Fluency

   1. Name a quadrilateral with exactly one pair of parallel sides.
   2. How many lines of symmetry does a rectangle have?
   3. Name a quadrilateral where all four sides are equal but angles are not 90°.
   4. True or False: all rectangles are parallelograms.

7. Calculate the perimeter of each shape: Fluency

   1. An equilateral triangle with side 7 cm
   2. A rectangle with length 13 cm and width 5 cm
   3. A rhombus with side length 9 cm
   4. An isosceles triangle with two equal sides of 10 cm and a base of 6 cm

8. A triangle has angles in the ratio 1 : 2 : 3. Understanding

   1. What are the three angles?
   2. What type of triangle is this based on its angles?
   3. Can a triangle have angles in the ratio 2 : 3 : 5? What type would it be?

9. A triangular garden has a base of 8 m. The two equal sides are each 10 m. Problem Solving

   1. What type of triangle is this?
   2. What is the perimeter of the garden?
   3. Fencing costs $15 per metre. How much will it cost to fence the garden?
   4. The base angles are each 66.4°. What is the apex angle?

10. Angle in a quadrilateral: the interior angles of a quadrilateral are x, 2x, x + 20, and 3x − 10. Problem Solving

    1. Write an equation using the fact that angles in a quadrilateral sum to 360°.
    2. Solve for x.
    3. Find all four angles.