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8th grade · Math · Unit 4 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.10(A); 8.10(B) · transformations that keep shapes congruent

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 4 of 15 in 8th grade Math, after Tessellations & Transformations and before Slope & Rate of Change.

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: Texas Education Agency (TEA)

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(-4, 5) is translated 1 unit right and 5 units down. What are the coordinates of A′?

    • (-5, 10)
    • (-3, 0)
    • (-5, 0)
    • (-3, 10)

  2. Question 2

    In congruent polygons, matching angles and sides are called…

    • adjacent
    • corresponding
    • opposite
    • parallel

  3. Question 3

    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

  4. Question 4

    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
    • RS
    • PQ
    • QR

  5. Question 5

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

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

  6. Question 6

    Which of these keeps a shape congruent?

    • enlarging it to double its size
    • shrinking it to half its size
    • stretching it taller
    • sliding it

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