Home
Class 9
MATHS
In Figure, the side B C\ of A B C is p...

In Figure, the side `B C\ ` of ` A B C` is produced to form ray `B D` as shown. Ray `C E` is drawn parallel to `B A` . Show directly, without using the angle sum property of a triangle that `A C D=\ /_A+/_b` and deduced that `/_A+/_B+/_C=180^0dot`

Text Solution

Verified by Experts

AB||CE `/_1=/_4`
AB||CE and BC is transverse
`/_2=/_5`(corresponding angles)
`/_1+/_2=/_4+/_5`
`/_A+/_B=/_ACD`
`/_A+/_B+/_C=/_ACD+/_C`
`/_A+/_B+/_C=180^@`.
Promotional Banner

Topper's Solved these Questions

  • TABULAR REPRESENTATION OF STATISTICAL DATA

    RD SHARMA|Exercise All Questions|62 Videos

Similar Questions

Explore conceptually related problems

In Figure,the side BC of hat grad ABC is produced to form ray BD as shown.Ray CE is drawn parallel to BA. Show directly,without using the angle sum property of a triangle that /_ACD=/_A+/_B and deduced that /_A+/_B+/_C=180^(@).

/_A+/_B+/_C+/_D+/_E=

A,B,C, are three angles of a triangle.If A-B=15^(0),B-C=30^(0), find /_A,/_B and /_C

A,B,C are the three angles of a triangle.If A-B=15^(0),B-C=30^(0), find /_A,/_B and /_C

Two triangles ABC and DEF such that /_A=/_D,/_B=/_E and /_C=/_F. Then

In a Delta ABC, if 2 /_A = 3 /_B = 6 /_C then calculate /_A, /_B and /_C .

In a Delta ABC; if 2/_A=3/_B=6/_C Determine /_A;/_B and /_C

In a parallelogram A B C D , if /_D=115^0, then write the measure of /_A

In Fig.81, side B C of A B C has been produced to D and C E B Adot If /_A B C=65^0,\ /_B A C=55^0, find /_A C E ,\ /_E C D\ a n d\ /_A C Ddot

RD SHARMA-TRIANGLE AND ITS ANGLES-All Questions
  1. The side B C of a A B C is produced on both sides. Show that the s...

    Text Solution

    |

  2. Sides B C ,\ C A\ a n d\ B A of a triangle A B C are produced to D ,\ ...

    Text Solution

    |

  3. In Figure, the side B C\ of A B C is produced to form ray B D as ...

    Text Solution

    |

  4. Prove that the angle between internal bisector of one base angle an...

    Text Solution

    |

  5. If in a "Delta"A B C ,(cosA)/a=(cosB)/b=(cosC)/c , then find the measu...

    Text Solution

    |

  6. The exterior angles, obtained on producing the base of a triangle b...

    Text Solution

    |

  7. An exterior angle of a triangle is 110^0 , and one of the interior opp...

    Text Solution

    |

  8. An exterior angle of a triangle is 110^0, and one of the interior ...

    Text Solution

    |

  9. Compute the value of x in each of the following figures: (ii) (iv...

    Text Solution

    |

  10. In Figure, A B divides /D A C in the ratio 1\ :3\ a n d\ A B=D Bdot De...

    Text Solution

    |

  11. A B C is a triangle. The bisector of the exterior angle at B and th...

    Text Solution

    |

  12. The bisectors of base angles of a triangle cannot enclose a right an...

    Text Solution

    |

  13. If the bisectors of the base angles of a triangle enclose an angle o...

    Text Solution

    |

  14. In Figure, A E bisects /C A D\ a n d\ /B=/Cdot Prove that A E||B C

    Text Solution

    |

  15. In a parallelogram, the bisectors of any two consecutive angles inte...

    Text Solution

    |

  16. Fill in the blanks to make the following statements true: Sum of the...

    Text Solution

    |

  17. Fill in the blanks to make the following statements true: Sum of th...

    Text Solution

    |

  18. Define a triangle.

    Text Solution

    |

  19. Write the sum of the angles of an obtuse triangle.

    Text Solution

    |

  20. Can the sum of the two angles of a triangle be less than the third ang...

    Text Solution

    |