Practice Maths

Topic Review — Congruence and Transformations

Mixed Practice — L48 – L50

This review covers all lessons in the Congruence and Transformations topic. Try each question before checking your answers.

Review Questions

  1. Congruent figures and congruence tests. Fluency

    1. State the four congruence tests for triangles and give the abbreviation for each.
    2. Two triangles each have sides 9 cm, 12 cm, 15 cm. State the congruence test and write the congruence statement: ▵ABC ≅ ▵___.
    3. ▵PQR ≅ ▵XYZ. PQ = 7 cm, ∠P = 48°. Find XY and ∠X.
    4. Are two triangles congruent if they have two equal angles? Explain.
    5. In ▵RST and ▵UVW: RS = UV = 6 cm, ST = VW = 10 cm, ∠RST = ∠UVW = 55°. Which test applies? Write the congruence statement.

  2. Transformations — finding images. Fluency

    1. Translate A(2, −3) by vector &binom{−5}{4}. Write the image coordinates.
    2. Reflect B(4, 6) in the x-axis.
    3. Reflect C(−3, 1) in the y-axis.
    4. Rotate D(5, 2) by 90° anticlockwise about the origin.
    5. Rotate E(3, −4) by 180° about the origin.
    6. Reflect F(7, 3) in the line y = x.

  3. Scale factor and similar figures. Understanding

    1. Two similar triangles: sides of first are 4 cm, 6 cm, 8 cm. Shortest side of second is 10 cm. Find the scale factor and the other two sides of the second triangle.
    2. A rectangle 5 cm × 12 cm is enlarged with scale factor 2.5. Find the new dimensions.
    3. A model ship is built to scale 1:200. The real ship is 160 m long. Find the model length in cm.
    4. Two similar shapes have areas in the ratio 9:25. What is the scale factor of their sides?

  4. Describe and apply transformations. Understanding

    1. Triangle A has vertices (1, 2), (3, 2), (2, 5). Triangle B has vertices (1, −2), (3, −2), (2, −5). Describe the single transformation from A to B.
    2. Triangle C has vertices (2, 1), (5, 1), (5, 4). Triangle D has vertices (−1, 2), (−1, 5), (−4, 5). Describe the single transformation from C to D.
    3. Point P(4, 3) is first translated by &binom{−6}{2}, then reflected in the y-axis. Find the final image.
    4. Which transformation would map a shape to its mirror image? Name an example from real life.

  5. Problem solving with congruence, transformations and similarity. Problem Solving

    1. ABCD is a parallelogram. Diagonal AC divides it into ▵ABC and ▵CDA.
      1. List all pairs of equal sides and equal angles using properties of a parallelogram.
      2. Prove that ▵ABC ≅ ▵CDA, stating the congruence test used.
    2. A photograph 8 cm × 12 cm is to be enlarged to fit a frame that is 30 cm wide.
      1. Find the scale factor needed.
      2. Find the required length of the frame.
      3. Is the enlarged photo similar to the original? Explain.
    3. A point P(3, 4) is reflected in the line y = x and then rotated 90° clockwise about the origin. What are the final coordinates? Is the result the same as first rotating then reflecting?
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