Home
Class 9
MATHS
In A B C and P Q R Figure, A B=P Q ,B C=...

In `A B C` and `P Q R` Figure, `A B=P Q ,B C=Q R` and `C B` and `R Q` are extended to `X` and `Y` respectively and `/_A B X` =`/_P Q Ydot` Prove that `A B C~=P Q Rdot` Figure

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|306 Videos

  • CONSTRUCTION

    RD SHARMA ENGLISH|Exercise All Questions|40 Videos

Similar Questions

Explore conceptually related problems

In ΔABC a n d\ Δ P Q R ,\ A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R Q are extended to X\ a n d\ Y respectively and /_A B X=/_P Q Y . Prove that A B C~=\ P Q R .

P and Q are points on the sides C A and C B respectively of A B C , right-angled at C . Prove that A Q^2+B P^2=A B^2+P Q^2 .

In Fig. 4.34, A ,\ B and C are points on O P ,\ O Q and O R respectively such that A B P Q and B C Q R . Show that A C P R . (FIGURE)

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

In Figure P Q || C D and P R || C B. Prove that ( A Q)/(Q D)=(A R)/(R B)dot

A B C is a triangle in which A B=A C\ a n d\ P is a point on A C . Through C a line is drawn to intersect B P produced at Q such that /_A B Q=\ /_A C Q . Prove that: /_A Q C=90^@+1/2/_B A C

In A B C , P and Q are points on sides A B and A C respectively such that P Q ||B C . If A P=3c m , P B=5c m and A C=8c m , find A Q .

In Figure, P , is any point on the chord B C of a circle such that A B=A P . Prove that C P=C Q .

In Figure, X\ a n d\ Y are the mid-points of A C\ a n d\ A B respectively, Q P || B C\ a n d\ C Y Q\ a n d\ B X P are straight lines. Prove that a r\ (\ A B P)=\ a r\ (\ A C Q) .

In Figure, A B C D\ a n d\ P Q R C are rectangles and Q is the mid-point of A C . Prove that D P=P C (ii) P R=1/2\ A C

RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. In Figure, X and Y are two points on equal sides A B and A C of a A B ...

    Text Solution

    |

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

    Text Solution

    |

  3. In A B C and P Q R Figure, A B=P Q ,B C=Q R and C B and R Q are extend...

    Text Solution

    |

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

    Text Solution

    |

  5. In a triangle the greater angle has the longer side opposite to it.

    Text Solution

    |

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

    Text Solution

    |

  7. If two sides of a triangle are unequal, the longer side has greater...

    Text Solution

    |

  8. The bisectors of base angles of a triangle cannot enclose a right a...

    Text Solution

    |

  9. ABCD is a square, X and Y are points on sides AD a...

    Text Solution

    |

  10. In figure, if P Q|P S ,P Q|| S R ,/S Q R=28^0 and /Q R T=65^0, then fi...

    Text Solution

    |

  11. If perpendiculars from any point with an angle on its arms are cong...

    Text Solution

    |

  12. In figure, if lines P Q and R S intersect at a point T such that P R T...

    Text Solution

    |

  13. A B C is a triangle is which B E and C F are, respectively, the perpen...

    Text Solution

    |

  14. Sides B C ,C A and BA of a triangle A B C are produced to D ,Q ,P resp...

    Text Solution

    |

  15. A B C is a triangle and D is the mid-point of B C . The perpendiculars...

    Text Solution

    |

  16. The side B C of a triangleA B C is produced on both sides. Show that t...

    Text Solution

    |

  17. P is a point equidistant from two lines l and m intersecting at a poin...

    Text Solution

    |

  18. If two parallel lines are intersected by a transversal, prove that ...

    Text Solution

    |

  19. If A B C is an isosceles triangle such that A B=A C and A D is an alti...

    Text Solution

    |

  20. If PS is the bisector of /Q P R and P T|Q R . Show that /T P S=1/2(/Q...

    Text Solution

    |