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About Congruence & Similarity — Class 8 IB

Determine congruence and similarity of figures using transformations and scale factors. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 6). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Congruence & Similarity — solved examples for Class 8 IB

Example 1easy

Two shapes are congruent if they have:
  1. A)Same shape only
  2. B)Same size only
  3. C)Same shape and size
  4. D)Same colour

Step-by-step solution

  1. Congruent shapes have the same shape and size.

Answer: Same shape and size

Example 2medium

Two similar triangles have corresponding sides in the ratio 3:5. If a side of the smaller triangle is 9 cm, find the corresponding side of the larger.
  1. A)12 cm
  2. B)15 cm
  3. C)18 cm
  4. D)21 cm

Step-by-step solution

  1. Find the scale factor.
    x=9×53=15 cmx = 9 \times \frac{5}{3} = 15 \text{ cm}

Answer: 15 cm

Example 3hard

Two similar triangles have areas in the ratio 16:49. Find the ratio of their corresponding sides.
  1. A)4:7
  2. B)2:7
  3. C)16:49
  4. D)8:21

Step-by-step solution

  1. Side ratio:
    16:49=4:7\sqrt{16}:\sqrt{49} = 4:7

Answer: 4:7

Practice questions on Congruence & Similarity

  1. Q1.easy

    Two shapes are similar if they have:
    1. A)Same shape only
    2. B)Same size only
    3. C)Same shape but possibly different size
    4. D)Same area
    Show answer

    Answer: Same shape but possibly different size

    Hint: Similar shapes are like scaled copies.

  2. Q2.easy

    Which congruence criterion requires two angles and the included side?
    1. A)SSS
    2. B)SAS
    3. C)ASA
    4. D)RHS
    Show answer

    Answer: ASA

    Hint: The side is between the two angles.

  3. Q3.easy

    Which criterion requires all three sides to be equal?
    1. A)SSS
    2. B)SAS
    3. C)ASA
    4. D)AAS
    Show answer

    Answer: SSS

    Hint: Three S's for three sides.

  4. Q4.medium

    Triangle ABC has AB = 5, angle A = 60°, angle B = 80°. Triangle DEF has DE = 5, angle D = 60°, angle E = 80°. Are they congruent? By which criterion?
    1. A)Yes, by SSS
    2. B)Yes, by ASA
    3. C)Yes, by SAS
    4. D)No, they are only similar
    Show answer

    Answer: Yes, by ASA

    Hint: Two angles and the included side match.

  5. Q5.medium

    A shape is enlarged by scale factor 3 from a centre of enlargement. If a vertex was 2 cm from the centre, how far is the image vertex?
    1. A)2 cm
    2. B)5 cm
    3. C)6 cm
    4. D)8 cm
    Show answer

    Answer: 6 cm

    Hint: Distance from centre is multiplied by the scale factor.

  6. Q6.medium

    Two similar rectangles have areas in what ratio if their sides are in the ratio 2:3?
    1. A)2:3
    2. B)4:9
    3. C)8:27
    4. D)4:6
    Show answer

    Answer: 4:9

    Hint: Areas scale as the square of the length ratio.

  7. Q7.hard

    A 6 m pole casts a shadow of 4 m. A nearby tree casts a shadow of 10 m. How tall is the tree?
    1. A)12 m
    2. B)15 m
    3. C)20 m
    4. D)24 m
    Show answer

    Answer: 15 m

    Hint: Use similar triangles formed by the objects and their shadows.

  8. Q8.hard

    In the figure, DE is parallel to BC in triangle ABC. AD = 4, DB = 6, AE = 5. Find EC.
    1. A)5
    2. B)6
    3. C)7.5
    4. D)10
    Show answer

    Answer: 7.5

    Hint: By the basic proportionality theorem (Thales): AD/DB = AE/EC.

  9. Q9.hard

    Two similar solids have corresponding edges in the ratio 2:5. What is the ratio of their volumes?
    1. A)2:5
    2. B)4:25
    3. C)8:125
    4. D)4:10
    Show answer

    Answer: 8:125

    Hint: Volume ratio = cube of the linear ratio.

These are 9 of the 60 questions available for Congruence & Similarity. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.