Home
Class 9
MATHS
Prove that Two right triangles are congr...

Prove that Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and one side of the other triangle.

Text Solution

Verified by Experts


Let the two triangles be `ABC` and `EFG`.
where `AC=EG ` (hypotenuse) and `AB=EF ` (one side equal).
We have to prove that `/_\ABC ` is congruent to `/_\EFG `.
`AC=EG ; `
`AB=EF; `
`/_ B=/_ E; `
Hence they are congruent by RHS.
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

Right Hand Side Congruence Condition (RHS) Two right triangles are congruent if the hypotenuse and one side of one triangle are respectively equal to the hypotenuse and ne side of the other triangle.

Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

THE SIDES-SIDES-SIDES (SSS) CONGRUENCE CONDITION Two triangles are congruent if the three sides of one triangle are respectively equal to the three sides of the other triangles.

If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent. 1. PL is an altitude from P of DeltaPQR on QR such that QL = LR. Then,

Consider the following statements : 1. Congruent triangles are similar. 2. Similar triangles are congruent. 3. If the hypotenuse and a side of one right triangle are equal to the hypotenuse and a side of another right triangle respectively, then the two right triangles are congruent. Which of the statements given above is/are correct ?

If in two right triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent. 1. In the figure, it is given that LM =MN, QM= MR, ML bot PQ and MN bot PR . then

Angle-Side-Angle (ASA) Congruence-Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.

Side Side Side(SSS) Congruence: Two triangles are congruent if the three sides of one triangle are equal to the corresponding three sides of the other triangle.

ASA CONGRUENCE CONDITION Two triangles are congruent if two angles and the included side of the one are respectively equal to the two angles and the included sides of the other.

RD SHARMA-CONGRUENT TRIANGLE -All Questions
  1. In figure, P Q R is a triangle in which P Q=P R and S is any point on ...

    Text Solution

    |

  2. If the bisector of the exterior vertical angle of a triangle be par...

    Text Solution

    |

  3. Prove that Two right triangles are congruent if the hypotenuse and o...

    Text Solution

    |

  4. In given figure the altitudes AD, BE and CF , the altitudes of triang...

    Text Solution

    |

  5. A point O is taken inside an equilateral four sided figure A B C D suc...

    Text Solution

    |

  6. In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points ...

    Text Solution

    |

  7. If two isosceles triangles have a common base, prove that the line ...

    Text Solution

    |

  8. A B C and D B C are two isosceles triangles on the same base B C ...

    Text Solution

    |

  9. Explain -Side Side Side(SSS) Congruence .

    Text Solution

    |

  10. A B C D is a parallelogram, if the two diagonals are equal, find th...

    Text Solution

    |

  11. In a A B C , it is given that A B=A C and the bisectors of /B a...

    Text Solution

    |

  12. A B C is a triangle in which /B =2 /CdotD is a point on B C s...

    Text Solution

    |

  13. In A B C ,\ /A=100^0a n d\ A B=A Cdot Find /B\ a n d\ /C

    Text Solution

    |

  14. In Figure, A B=A C\ a n d\ /A C D=120^0dot Find /A

    Text Solution

    |

  15. Prove that measure of each angle of an equilateral triangle is 60^0d...

    Text Solution

    |

  16. In Figure O is the mid-point of A B\ a n d\ C Ddot Prove that \ A O C...

    Text Solution

    |

  17. In Figure, it is given that A B=C F ,\ E F=B D\ a n d\ /A F E=\ /C B...

    Text Solution

    |

  18. In Figure, it is given that A E=A D\ a n d\ B D=C Edot Prove that A...

    Text Solution

    |

  19. Given: In /\ABC and /\PQR, A B=P Q ,\ B C=Q R\ a n d\ C B\ a n d\ R ...

    Text Solution

    |

  20. In Figure, X ,\ Y\ are two points on equal sides A B\ a n d\ A C of...

    Text Solution

    |