Home
Class 9
MATHS
In two triangles A B C\ a n d\ A D C , i...

In two triangles `A B C\ a n d\ A D C ,` if `A B=A D\ a n d\ B C=C Ddot` Are they congruent?

Text Solution

Verified by Experts

Solution
The given triangles will be congruent by the 'SSS' congruency.
'AB=AD' (Given)
'BC=CD' (Given)
Thus, according to the figure which will be formed -
In `/_\ABC` and `/_\ADC`
'AB = AD' (Given)
'BC = CD' (Given)
'AC= AC' (Common Side) -
Therefore, By the side side side '(SSS)' congruency -
`/_\ABC = /_\ADC`
Hence Proved
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    RD SHARMA|Exercise All Questions|306 Videos

  • CONSTRUCTION

    RD SHARMA|Exercise All Questions|29 Videos

Similar Questions

Explore conceptually related problems

Fill in the blanks in the following so that each of the following statements is true Sides opposite to equal angles of a triangle are ....... Angle opposite to equal sides of a triangle are ....... In an opposite to equal sides of a triangle are ....... In a A B C if /_A=/_C , then A B= ..... If altitudes C E a n d B F of a triangle A B C are equal, then A B= ........ In an isosceles triangle A B C with A B=A C , if B D a n d C E are its altitudes, then B D is .......... C E In right triangles A B C a n d D E F , if hypotenuse A B=E F and side A C=D E , then A B C ~= ....

In Figure, A B_|_B E\ a n d\ F E\ _|_B Edot If B C=D E\ a n d\ A B=E F , then A B D is congruent to: E F C (b) E C F (c) C E F (d) F E C

If A B C and DEF are two triangles such that A B C ~= F D E a n d A B=5c m , /_B=40^0 a n d /_A=80^0dot Then, which of the following is true? D F=5c m , /_F=60^0 (b) D E=5c m , /_E=60^0 D F=5 c m , /_E=60^0 (d) D E=5c m , /_D=40^0

In a parallelogram A B C D , write the sum of angle A\ a n d\ B

Any point D is taken in the base B C of a triangle A B C\ a n d\ A D is produced to E , making D E equal to A Ddot Show that a r\ ( B C E)=a r( A B C)

If in two triangles A B C and D E F , (A B)/(D E)=(B C)/(F E)=(C A)/(F D) , then F D E C A B (b) F D E A B C (c) C B A F D E (d) B C A F D E

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

In quadrilateral A B C D show in Figure. A B D C a n d A D_|_A Bdot Also, A B=8m , D C=B C=5mdot Find the area of the quadrilateral.

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

In Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C

RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. In two triangles A B C\ a n d\ D E F , it is given that /A=/D ,\ /B=/E...

    Text Solution

    |

  2. If A B C\ a n d\ D E F are two triangles such that A C=2. 5\ c m ,\...

    Text Solution

    |

  3. In two triangles A B C\ a n d\ A D C , if A B=A D\ a n d\ B C=C Ddot A...

    Text Solution

    |

  4. In triangle A B C\ a n d\ C D E , if A C=C E ,\ B C=C D ,\ /A=60^0,\ /...

    Text Solution

    |

  5. A B C is an isosceles triangle in which A B=A CdotB E\ a n d\ C F a...

    Text Solution

    |

  6. Find the measure of each angle of an equilateral triangle.

    Text Solution

    |

  7. C D E is an equilateral triangle formed on a side C D of a square A ...

    Text Solution

    |

  8. Show that the sum of the three altitudes of a triangle is less than ...

    Text Solution

    |

  9. In Figure, if A B=A C\ a n d\ /B=/Cdot Prove that B Q=C P

    Text Solution

    |

  10. If A N C~= L K M , then side of L K M equal to side A C\ of A B C ...

    Text Solution

    |

  11. If A B C\ ~= A C B , then A B C is isosceles with A B=A C (b) A B=B...

    Text Solution

    |

  12. If A B C~= P Q R and A B C is not congruent to R P Q , then which o...

    Text Solution

    |

  13. In triangles A B C\ a n d\ P Q R three equality relations between so...

    Text Solution

    |

  14. In triangles A B C\ a n d\ P Q R , if /A=/R ,\ /B=/P\ a n d\ A B=R P ,...

    Text Solution

    |

  15. If P Q R\ ~= E F D , then E D= PQ (b) QR (c) PR (d) None of these

    Text Solution

    |

  16. If P Q R\ ~= E F D , then /E= /P (b) /Q (c) /R (d) None of ...

    Text Solution

    |

  17. In a A B C , if A B=A C\ a n d\ B C is produced to D such that /A C D...

    Text Solution

    |

  18. In an isosceles triangle, if the vertex angle is twice the sum of th...

    Text Solution

    |

  19. D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B re...

    Text Solution

    |

  20. Which of the following is not a criterion for congruence of triangle...

    Text Solution

    |