Trapezoids

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

Figure P Q R S is shown where side P Q and R S are parallel but not congruent. Side P S has positive slope and side Q R has negative slope

In looking at the picture you will see PQ is parallel to segment SR

Those two segments are the bases.

Segment PS and segment QR are the legs ∠R and ∠S are base angles.

Trapazoid P Q R S is drawn again, this time with diagonals shown.

Segments SQ and RP are called diagonals

∠P is opposite ∠R and ∠S is opposite ∠Q

Go to Geogebra: Trapezoids to find out more about trapezoids.

Trapezoids and Parallel

Because the bases of a trapezoid are formed by parallel lines, the consecutive angles on the same legs of the trapezoid have a special relationship. They are same side interior angles. Therefore, just as with same side interior angles angles on the same of a transversal cutting two parallel lines formed by a transversal cutting two parallel lines, consecutive angles on the legs of a trapezoid are supplementary sum to 180° .

Trapazoid A B C D is shown, where side A B and parallel to side C D. Angle B and angle D are adjacent and highlighted

Go to Geogebra: Consecutive Angles to find out more!

Your Turn!

1. Segments AB and CD are __________.

  1. bases
  2. consecutive angles
  3. base angles
  4. diagonals
  5. legs

Answer: A - bases; AB and CD are parallel, so they form the base of the trapezoid.

2. Segments DA and BC are __________.

  1. bases
  2. consecutive angles
  3. base angles
  4. diagonals
  5. legs

Answer: E - legs ; DA and BC are not parallel, so they form the legs of the trapezoid.

3. Segments AC and BD are __________.

  1. bases
  2. consecutive angles
  3. base angles
  4. diagonals
  5. legs

Answer: D - diagonals; AC and BD cut through the interior of the trapezoid, so they are diagonals.

4. ∠A and ∠D are ________________.

  1. bases
  2. consecutive angles
  3. base angles
  4. diagonals
  5. legs

Answer: B - consecutive angles; Angle A and Angle D share a leg of the trapezoid as a side, so they are consecutive angles.

5. ∠C and ∠D are ____________.

  1. bases
  2. consecutive angles
  3. base angles
  4. diagonals
  5. legs

Answer: C - base angles; Angle C and Angle D share a base of the trapezoid as a side, so they are base angles.

 

Previous Page