Classifying Triangles & Quadrilaterals — Solutions

1. Identify Each Triangle — By Sides

   1. Equilateral ▶ View Solution
   2. Right-angled ▶ View Solution
   3. Isosceles ▶ View Solution
   4. Scalene ▶ View Solution
   5. Tick marks go on: The two equal sides (not the base) ▶ View Solution

2. Classify Triangles — By Angles

   1. 60°, 60°, 60°: Acute ▶ View Solution
   2. Contains 90°: Right-angled ▶ View Solution
   3. Contains 110°: Obtuse ▶ View Solution
   4. 40°, 70°, 70°: Acute ▶ View Solution
   5. Can a triangle have both a right angle and an obtuse angle? No — impossible (they would exceed 180° combined) ▶ View Solution

3. Name Each Quadrilateral

   1. Two pairs of parallel sides, no right angles: Parallelogram ▶ View Solution
   2. Four right angles: Rectangle ▶ View Solution
   3. All four sides equal, no right angles: Rhombus ▶ View Solution
   4. Exactly one pair of parallel sides: Trapezium ▶ View Solution
   5. Two pairs of adjacent equal sides: Kite ▶ View Solution

4. True or False?

   1. Every square is a rectangle: True ▶ View Solution
   2. Every rectangle is a square: False ▶ View Solution
   3. A rhombus always has right angles: False ▶ View Solution
   4. Every square is a rhombus: True ▶ View Solution
   5. A trapezium has two pairs of parallel sides: False ▶ View Solution

5. Isosceles Triangle Investigation

   1. Base angles if apex = 40°: 70° each ▶ View Solution
   2. Angle type (40°, 70°, 70°): Acute ▶ View Solution
   3. Is Tran correct that isosceles must be acute? Incorrect — an isosceles triangle can be obtuse ▶ View Solution
   4. Top angle if base angles are both 60°: 60° — equilateral triangle ▶ View Solution

6. The Quadrilateral Family

   1. Which shapes are parallelograms? Rectangle, Square, Rhombus, and Parallelogram ▶ View Solution
   2. Which have all four sides equal? Square and Rhombus ▶ View Solution
   3. Which have four right angles? Rectangle and Square ▶ View Solution
   4. Is Maya correct that a square is both a rectangle and a rhombus? Yes — a square satisfies the properties of both ▶ View Solution

7. Double Classification

   1. All sides equal; all angles 60°: Equilateral and Acute ▶ View Solution
   2. Two equal legs; one 90° angle: Isosceles and Right-angled ▶ View Solution
   3. 30°, 40°, 110°: Scalene and Obtuse ▶ View Solution
   4. 40°, 70°, 70°: Isosceles and Acute ▶ View Solution

8. Name the Shape From Its Properties

   1. Four equal sides; no right angles: Rhombus ▶ View Solution
   2. Exactly one pair of parallel sides: Trapezium ▶ View Solution
   3. Two pairs of adjacent equal sides (unequal pairs): Kite ▶ View Solution
   4. Four equal sides; four right angles: Square ▶ View Solution

9. Architecture and Shapes

   1. No equal sides; one 90° angle: Scalene and Right-angled ▶ View Solution
   2. Isosceles, apex = 100°: Base angles = 40° each — Obtuse triangle ▶ View Solution
   3. One pair of parallel sides — name and difference from parallelogram: Trapezium — has only one pair of parallel sides, not two ▶ View Solution

10. Shape Sorting Challenge

    1. Shapes with at least one pair of parallel sides: Shapes 2 (Rectangle), 3 (Rhombus), and 4 (Trapezium) ▶ View Solution
    2. Shapes with at least one pair of equal sides: Shapes 1, 2, 3, and 4 ▶ View Solution
    3. Which shape belongs to the parallelogram family and why? Shape 3 (Rhombus) — two pairs of parallel sides and all four sides equal ▶ View Solution