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Grade 8 · Math · Unit 10 of 11

Congruent Shapes

Slides, flips and turns that keep a shape the same

What your child practises

Recognizing congruent shapes, matching corresponding sides and angles, and finding the coordinates of a point after a slide, flip or turn.

Nunavut Curriculum approved guide: Alberta Mathematics K–9 (2007), Shape and Space · congruence of polygons and the coordinates of images after translations, reflections and rotations

How we explain it

Children can open this short lesson before they practise.

  1. Congruent shapes have the same size and shape.
  2. Slides, flips and turns keep a shape congruent.
  3. Matching sides and angles are equal.

Example: A triangle is slid across the page. Is the new triangle congruent? A slide does not change size or shape. So the triangles match. Answer: Yes

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Point A(-3, -4) is rotated 180° about the origin. What are the coordinates of A′?

    • (3, -4)
    • (-3, 4)
    • (-4, -3)
    • (3, 4)

  2. Question 2

    Polygon ABCD is congruent to polygon PQRS, with A matching P, B matching Q and so on. If AB = 5 cm, which side must also be 5 cm?

    • SP
    • QR
    • PQ
    • RS

  3. Question 3

    A shape is reflected, then rotated. Is the final image congruent to the original?

    • no, a reflection changes the size
    • yes, each move keeps the size and shape
    • only if the rotation is 180°
    • no, only one move can be used

  4. Question 4

    Triangle ABC is translated to make triangle A′B′C′. Which statement is true?

    • the triangles have different areas
    • AB is shorter than A′B′
    • ∠A is larger than ∠A′
    • ∠A = ∠A′ and AB = A′B′

  5. Question 5

    Point A(6, 3) is reflected in the y-axis. What are the coordinates of A′?

    • (-6, 3)
    • (-6, -3)
    • (3, 6)
    • (6, -3)

  6. Question 6

    Two triangles have sides 3 cm, 4 cm, 5 cm and 3 cm, 4 cm, 6 cm. Are they congruent?

    • no, one pair of sides is different
    • yes, they are both triangles
    • only if their angles are 90°
    • yes, two sides match

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