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8th grade · Math · Unit 12 of 19

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.

New York State Learning Standards learning standard: NY-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 New York

In the New York State Learning Standards, this is unit 12 of 19 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: New York State Education Department (NYSED)

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

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

  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?

    • RS
    • SP
    • QR
    • PQ

  3. Question 3

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

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

  4. Question 4

    In congruent polygons, matching angles and sides are called…

    • adjacent
    • opposite
    • parallel
    • corresponding

  5. Question 5

    Point A(-4, -3) is rotated 90° clockwise about the origin. What are the coordinates of A′?

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

  6. Question 6

    Congruent shapes have the same…

    • number of sides only
    • size and shape
    • color only
    • size only

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