Understanding Elementary Shapes

Obtuse angle

Step 1: We need to classify an angle of 135°. Step 2: Recall: Acute < 90°, Right = 90°, Obtuse is between 90° and 180°, Straight = 180°, Reflex > 180°. Step 3: Compare: 90° < 135° < 180°. So it falls in the obtuse range. Final Answer: 135° is an obtuse angle. Students often confuse obtuse with reflex. Remember obtuse is strictly between 90° and 180°.

Equilateral triangle

Step 1: We are told all three sides of the triangle are equal. Step 2: Recall the classification by sides: Equilateral = all 3 sides equal. Isosceles = exactly 2 sides equal. Scalene = all 3 sides different. Step 3: Since all three sides are equal, the triangle is equilateral. Final Answer: A triangle with all three sides equal is called an equilateral triangle. In an equilateral triangle, all three angles are also equal (each = 60°).

Isosceles triangle

Step 1: We are given PQ = 5 cm, QR = 5 cm, PR = 7 cm. Step 2: Compare the sides: PQ = QR = 5 cm (two sides are equal), but PR = 7 cm is different. Step 3: A triangle with exactly two equal sides is called an isosceles triangle. Step 4: Since two sides (PQ and QR) are equal and one side (PR) is different, this is an isosceles triangle. Final Answer: Triangle PQR is an isosceles triangle.

6

Step 1: We need to recall the names of polygons based on number of sides. Step 2: Triangle = 3 sides, Quadrilateral = 4 sides, Pentagon = 5 sides, Hexagon = 6 sides, Heptagon = 7 sides, Octagon = 8 sides. Step 3: The prefix 'hex' means six (like hexagonal honeycomb cells). Final Answer: A hexagon has 6 sides. A helpful trick: honeybees build hexagonal (6-sided) cells in their honeycombs!