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8th grade · Math · Unit 11 of 17

Congruent Shapes

Slides, flips and turns that keep a shape the same

What your child practices

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

Arizona Academic Standards learning standard: 8.G.A.2 · congruence through rotations, reflections and translations

How we explain it

Children can open this short lesson before they practice.

  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

Congruent Shapes in Arizona

In the Arizona Academic Standards, this is unit 11 of 17 in 8th grade Math, after Equations with Brackets and before Exponent Rules.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Arizona Department of Education

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

    A triangle is flipped over a line. Is the image congruent to the original?

    • no, it is a different size
    • no, it has different angles
    • only if it is a square
    • yes

  2. Question 2

    A 4 cm by 6 cm rectangle and a 6 cm by 4 cm rectangle are…

    • congruent
    • similar but never congruent
    • not congruent, because 4 ≠ 6
    • not congruent, because they point different ways

  3. Question 3

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

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

  4. Question 4

    In congruent polygons, matching angles and sides are called…

    • parallel
    • opposite
    • adjacent
    • corresponding

  5. Question 5

    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?

    • PQ
    • QR
    • RS
    • SP

  6. Question 6

    Point A(2, 5) is rotated 90° counterclockwise about the origin. What are the coordinates of A′?

    • (-5, 2)
    • (-2, -5)
    • (2, -5)
    • (5, -2)

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