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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.

Alaska content standards learning standard: 8.G.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 Alaska

In the Alaska content 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: Alaska Department of Education and Early Development

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(8, 1) is rotated 180° about the origin. What are the coordinates of A′?

    • (-8, -1)
    • (1, 8)
    • (-8, 1)
    • (8, -1)

  2. Question 2

    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′

  3. Question 3

    A turn about a point is called a…

    • rotation
    • translation
    • reflection
    • dilation

  4. Question 4

    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
    • only if their angles are 90°
    • yes, they are both triangles
    • yes, two sides match

  5. Question 5

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

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

  6. Question 6

    In congruent polygons, matching angles and sides are called…

    • corresponding
    • parallel
    • opposite
    • adjacent

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