We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

In this section ,we will discuss some trapezoid and its theorems.Trapezoid is a quadrilateral with at least one pair of parallel sides. AB || CD. (if there are two pairs of parallel lines then it is a parallelogram)

When non-parallel sides in trapezoid are equal then it is know ans isosceles trapezoid.

Statements |
Reasons |

1) ABCD is a trapezoid. | 1) Given |

2) AB || CD | 2) Given |

3) AD = BC | 3) Given |

4) DA || CE | 4) By construction |

5) ADCE is a parallelogram. | 5) By Properties of parallelogram. |

6) DA = CE and DC = AE | 6) By properties of parallelogram. |

7) BC = CE | 7) BC = AD and AD = CE (Transitive property) |

8) ∠CEB ≅ &CBE | 8) If BC ≅ CE then angle opposite to them are congruent. |

9) ∠DAB ≅ ∠ABC | 9) property of parallelogram and linear pair angles |

10) ∠A + ∠D = 180 and ∠B + ∠C = 180 | 10) Interior angles on the same side of the transversal are supplementary. |

11) ∠A + ∠D = ∠C + ∠B | 11) Transitivity ( Right sides are same so left sides are equal) |

12) ∠D = ∠C | 12) From above (∠A = ∠B) |

PQ||RS and PS = QR, so trapezoid PQRS is an isosceles trapezoid.

In isosceles trapezoid, base angles are equal.(trapezoid and its theorems)

∠S = ∠R and ∠P = ∠Q

But ∠S = 60

∴ ∠R = 60

Let ∠P = ∠Q = x

Sum of all the angles in a quadrilateral is 360.

∴ ∠P + ∠Q + ∠S + ∠R = 360

x + x + 60 + 60 = 360

2x +120 = 360

2x = 360 -120

2x = 240

∴ x = 240/2

x = 120

∠P = ∠Q = 120

__________________________________________________________________

Some important theorems of trapezoids are given below :

Theorems |

1. A trapezoid is isosceles if and only if the base angles are congruent. |

2. A trapezoid is isosceles if and only if the diagonals are congruent. |

3. If a trapezoid is isosceles, the opposite angles are supplementary. |

The median (or mid-segment) of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases. |

Never assume that a trapezoid is isosceles unless you are given (or can prove) that information. |

1) In a trapezoid ABCD,AB|| CD and BC = AD. If m∠C=65

2) PQRS is a trapezium in which PQ || RS. If ∠P = ∠Q = 40, find the measures of other two angles.

3) In trapezoid ABCD, ∠B= 120

4) In a quadrilateral HELP, if EP = LH then what type of quadrilateral it is?

5) In a quadrilateral, the angles are in the ratio of 4:5:3:6.Find the measures of each angles.

6) If three angles in the trapezoid are 130

7) Draw a isosceles trapezoid named PQRS, PS||QR and PQ = SR.

• Introduction to Quadrilateral

• Types of Quadrilateral

• Properties of Quadrilateral

• Parallelogram and its Theorems

• Rectangle and its Theorems

• Square and its Theorems

• Rhombus and its Theorems

• Trapezoid and its Theorems

• Kite and its Theorems

• Mid Point Theorem

Home Page

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers