**Covid-19 has led the world to go through a phenomenal transition .**

**E-learning is the future today.**

**Stay Home , Stay Safe and keep learning!!!**

AB ≅ DE, BC ≅ EF and ∠B ≅ ∠E

∴ ΔABC ≅ Δ DEF by SAS

Statements |
Reasons |

1) AB = AC | 1) Given |

2) AD is a bisector | 2) By construction |

3) ∠BAD = ∠CAD | 3) By definition of angle bisector |

4) AD = AD | 4) Reflexive (common side) |

5) ΔABD ≅ ΔACD | 5) SAS Postulate |

6) ∠B = ∠C | 6) CPCTC |

1) O is the mid point of AB and CD. Prove that

i) ΔAOC ≅ ΔBOD ii) AC = BD and iii) AC || BD .

Statements |
Reasons |

1) O is the mid point. | 1) Given |

2) AO = OB | 2) By definition of mid point. |

3) ∠AOC = ∠BOD | 3) Vertically opposite angles |

4) CO = OD | 4) By definition of mid point. |

5) ΔAOC ≅ ΔBOD | 5) SAS postulate |

6) AC = BD | 6) CPCTC |

7) ∠CAO = ∠DBO | 7) CPCTC |

8) AC || BD | 8) If alternate interior angles are congruent then the lines are parallel. |

2) If D is the mid point of the hypotenuse AC of a right triangle ABC, prove that BD = ½ AC.

Statements |
Reasons |

1) AD = DC | 1) Given |

2) BD = DE | 2) By construction |

3) ∠ADB = ∠CDE | 3) Vertically opposite angles |

4) ΔADB ≅ ΔCDE | 4) By SAS postulate |

5) EC = AB and ∠CED = ∠ABD | 5) CPCTC |

6) CE || AB | 6) If alternate interior angles are congruent then the lines are parallel |

7) ∠ABC + ∠ECB = 180 | 7) Angles formed on the same side of transveral are supplementary. |

8) 90 + ∠ECB = 180 | 8) Since ∠B = 90 given |

9) ∠ECB = 180 -90 = 90 | 9) By subtraction property |

10) AB = EC | 10) From (5) |

11) BC = CB | 11) Reflexive (Common side) |

12) ∠ABC = ∠ECB | 12) Each 90^{0} |

13) ΔABC ≅ ΔECB | 13) SAS postulate |

14) AC = BE | 14) CPCTC |

15) 1/2AC = 1/2BE ⇒ 1/2AC = BD | 15) Multiply by 1/2 but 1/2BE = BD by mid point definition. |

•

•

•

•

•

**Covid-19 has affected physical interactions between people.**

**Don't let it affect your learning.**

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