Draw Shapes

Grade 7 · geometry · 100 practice problems · read aloud

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Drawing Shapes in Geometry

What is it and Why is it Useful? 🎯

Drawing shapes means creating accurate geometric figures using tools like a ruler, protractor, and compass. It's the foundation for architecture, engineering, and design. Mastering this helps you understand properties like angles, symmetry, and area.

How to Draw Shapes: A Step-by-Step Guide

  1. Identify: Know which shape you need to draw and its properties (e.g., a triangle has 3 sides).
  2. Plan: Decide what tools you need (ruler for straight lines, protractor for angles).
  3. Start Drawing: Begin with a base line. Use your tools to add sides and angles accurately.
  4. Check: Verify your shape has the correct number of sides and angle measurements.
  5. Label: Mark vertices (corners) with letters and note side lengths or angle sizes.

Visual Examples

Example 1: Drawing a Square

Let's draw a square with 5 cm sides.

  1. Use a ruler to draw a horizontal line 5 cm long. Label the ends A and B.
  2. At point A, use a protractor to measure a 90° angle upwards from line AB.
  3. Draw a vertical line 5 cm long from A. Label the end D.
  4. Repeat step 2 at point B to draw another 5 cm vertical line. Label the end C.
  5. Connect points D and C with a ruler to complete the square.

Example 2: Drawing a Triangle

Draw a triangle with sides 6 cm, 5 cm, and 4 cm.

  1. Draw the longest side (6 cm). Label ends A and B.
  2. Set your compass to 5 cm. Place the point on A and draw an arc.
  3. Set your compass to 4 cm. Place the point on B and draw an arc that crosses the first arc.
  4. Label the intersection point C. Connect C to A and C to B to complete the triangle.

Common Mistakes to Avoid

Inaccurate Measurements: Always double-check your ruler and protractor readings. A small error at the start makes the whole shape wrong.

Rushing the Process: Drawing shapes takes patience. Don't skip steps like planning or checking your work.

Forgetting Properties: Remember that all angles in a triangle add to 180°, and a square has four equal sides and four 90° angles.

Tips & Tricks

Use a Sharp Pencil: A fine line is more accurate than a thick, dark one.

Triangle Sum Check: After drawing a triangle, measure its three angles. They should always add up to 180°.

Compass Care: Ensure your compass is tight so the radius doesn't change while you're drawing arcs.

How to Practice

  • Start Simple: Practice drawing basic shapes like squares and equilateral triangles.
  • Use Grid Paper: This helps you draw straight lines and right angles more easily.
  • Challenge Yourself: Try drawing complex shapes by breaking them into simpler ones (e.g., a house from a square and a triangle).
  • Real-World Connection: Find shapes around you (a book, a window) and try to draw them to scale.

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 √(144) + 3² × 2 = ?

Hint: Remember to follow the order of operations when evaluating expressions with multiple operations.

Show the answer

Answer: 30

  1. Identify the operations in the expression: √(144) + 3² × 2
  2. Evaluate the square root first. √(144) = 12 So now we have: 12 + 3² × 2
  3. Evaluate the exponent. 3² = 9 So now we have: 12 + 9 × 2
  4. Perform multiplication before addition (order of operations: PEMDAS/BODMAS). 9 × 2 = 18 So now we have: 12 + 18
  5. Perform the addition. 12 + 18 = 30 Final Answer: 30

Let's solve step-by-step.

2 (3/4 + 2/3) × 12 = ?

Hint: When working with fractions inside parentheses, first find a common denominator to add them together. Then multiply the result by the whole number outside the parentheses.

Show the answer

Answer: 17

  1. Add the fractions inside the parentheses. We have 3/4 + 2/3. To add these, we need a common denominator. The least common denominator of 4 and 3 is 12.
  2. Convert each fraction to have denominator 12. 3/4 = (3 × 3)/(4 × 3) = 9/12 2/3 = (2 × 4)/(3 × 4) = 8/12
  3. Add the converted fractions. 9/12 + 8/12 = (9 + 8)/12 = 17/12
  4. Now the expression is (17/12) × 12. Multiplying a fraction by its denominator simplifies nicely: (17/12) × 12 = 17 × (12/12) = 17 × 1 = 17 Final Answer: 17

3 (-3)² + 2 × (-4) - 5 = ?

Hint: Remember the order of operations and how negative numbers behave with exponents

Show the answer

Answer: -4

  1. Calculate (-3)² = 9 (negative times negative gives positive)
  2. Calculate 2 × (-4) = -8
  3. Rewrite the expression: 9 + (-8) - 5
  4. Add 9 + (-8) = 1
  5. Subtract 5: 1 - 5 = -4

The answer is -4.

4 (-3)² + 4 × (-5) - √81 = ?

Hint: Remember the order of operations and how negative numbers behave with exponents

Show the answer

Answer: -20

  1. Evaluate (-3)² = 9 (negative times negative is positive)
  2. Evaluate 4 × (-5) = -20
  3. Evaluate √81 = 9
  4. Combine all terms: 9 + (-20) - 9
  5. 9 + (-20) = -11
  6. -11 - 9 = -20

The answer is -20.

5 (-3)² + 4 × (-5) - √(81) = ?

Hint: Remember the order of operations and how negative numbers behave with exponents

Show the answer

Answer: -20

  1. Calculate (-3)² = 9 (negative times negative gives positive)
  2. Calculate 4 × (-5) = -20
  3. Calculate √(81) = 9
  4. Combine all parts: 9 + (-20) - 9
  5. 9 - 20 = -11
  6. -11 - 9 = -20

The answer is -20.

6 (3/4 + 2/3) ÷ (5/6 - 1/2) = ?

Hint: When working with fractions, find common denominators before adding or subtracting, and remember that dividing by a fraction is the same as multiplying by its reciprocal.

Show the answer

Answer: 17/4

  1. First, add 3/4 and 2/3. The common denominator is 12. 3/4 = 9/12 and 2/3 = 8/12. So, 9/12 + 8/12 = 17/12.
  2. Next, subtract 1/2 from 5/6. The common denominator is 6. 5/6 = 5/6 and 1/2 = 3/6. So, 5/6 - 3/6 = 2/6, which simplifies to 1/3.
  3. Now the expression is (17/12) ÷ (1/3). Dividing by a fraction is the same as multiplying by its reciprocal. So, 17/12 × 3/1 = (17 × 3) / (12 × 1) = 51/12.
  4. Simplify 51/12 by dividing the numerator and denominator by 3. 51 ÷ 3 = 17 and 12 ÷ 3 = 4. So, the simplified answer is 17/4. The final answer is 17/4.
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