Skills · Geometry · Polygons & Quadrilaterals

Rectangles, rhombuses, squares and trapezoids

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. rectangle ABCD, diagonals meeting at E: BE ?, AC 14ABCDE?
    ABCD is a rectangle. AC = 14. Find the length marked ?.
  2. isosceles trapezoid ABCD, bases AB and DC: ∠D ?, ∠C 119°ABCD?119°
    ABCD is an isosceles trapezoid. Find the measure of the angle marked ?.
  3. rhombus ABCD, diagonals meeting at E: ∠1 is ∠ABEABCDE1
    ABCD is a rhombus. m∠1 = 65°. Find m∠ABC.
  4. trapezoid ABCD, bases AB and DC, midsegment MN: MN 10, AB ?, DC 7ABCDMN10?7
    ABCD is a trapezoid with midsegment MN. Find the length marked ?.
  5. rectangle ABCD, diagonals meeting at E: AE 18, BD ?ABCDE18
    ABCD is a rectangle. Find BD.
  6. isosceles trapezoid ABCD, bases AB and DC: ∠D ?, ∠C 102°ABCD?102°
    ABCD is an isosceles trapezoid. Find the measure of the angle marked ?.
  7. trapezoid ABCD, bases AB and DC, midsegment MN: MN 16, AB ?, DC 14ABCDMN16?14
    ABCD is a trapezoid with midsegment MN. Find the length marked ?.
  8. rhombus ABCD, diagonals meeting at E: ∠1 is ∠BAE, ∠2 is ∠ABEABCDE12
    ABCD is a rhombus. m∠1 = 35°. Find m∠2.

Answer key

  1. 7 units
  2. 119°
  3. 130°
  4. 13 units
  5. 36 units
  6. 102°
  7. 18 units
  8. 55°

Sample Sheet · Level 3

  1. rhombus ABCD, diagonals meeting at E: ∠1 is ∠BAE, ∠2 is ∠ABEABCDE12
    ABCD is a rhombus. m∠1 = (9x − 10)° and m∠2 = (4x + 35)°. Find m∠2.
  2. trapezoid ABCD, bases AB and DC, midsegment MN: MN 2x − 30, AB x − 7, DC 7ABCDMN2x − 30x − 77
    ABCD is a trapezoid with midsegment MN. Find AB.
  3. rectangle ABCD, diagonals meeting at E: BE 4x − 28, AC 3x − 1ABCDE4x − 28
    ABCD is a rectangle. AC = 3x − 1. Find BE.
  4. trapezoid ABCD, bases AB and DC, midsegment MN: MN 2x − 18, AB 21, DC x − 3ABCDMN2x − 1821x − 3
    ABCD is a trapezoid with midsegment MN. Find DC.
  5. rectangle ABCD, diagonals meeting at E: BE 4x − 20, AC 6x − 20ABCDE4x − 20
    ABCD is a rectangle. AC = 6x − 20. Find BE.
  6. isosceles trapezoid ABCD, bases AB and DC: ∠D (5x + 26)°, ∠C (8x − 28)°ABCD(5x + 26)°(8x − 28)°
    ABCD is an isosceles trapezoid. Find m∠D.
  7. isosceles trapezoid ABCD, bases AB and DC: ∠A (5x − 29)°, ∠B (2x + 34)°ABCD(5x − 29)°(2x + 34)°
    ABCD is an isosceles trapezoid. Find m∠B.
  8. rhombus ABCD, diagonals meeting at E: ∠1 is ∠ABEABCDE1
    ABCD is a rhombus. m∠1 = (9x − 20)° and m∠ABC = (7x + 48)°. Find m∠1.

Answer key

  1. 55°
  2. 13 units
  3. 16 units
  4. 15 units
  5. 20 units
  6. 116°
  7. 76°
  8. 52°

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