GradeMap

Grade 8 · Math · Unit 11 of 13

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.

Alberta Curriculum learning outcome: SS6 · congruence of polygons and the coordinates of images after translations, reflections and rotations

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)
    Show answer

    (3, 4)

    Hint: A half turn changes the sign of both coordinates.

  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
    Show answer

    PQ

    Hint: Corresponding sides are in the same position: AB matches PQ.

  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
    Show answer

    yes, each move keeps the size and shape

    Hint: A combination of slides, flips and turns still gives a congruent image.

  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′
    Show answer

    ∠A = ∠A′ and AB = A′B′

    Hint: A translation moves every point the same way, so lengths and angles do not change.

  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)
    Show answer

    (-6, 3)

    Hint: A reflection in the y-axis flips the point across it. The x-coordinate changes sign.

  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
    Show answer

    no, one pair of sides is different

    Hint: All three pairs of matching sides must be equal.

More Grade 8