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**Exercise 6.1 : ** Solutions of Questions on Page Number : **116**

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**Exercise 6.2 : ** Solutions of Questions on Page Number : **118**

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**Exercise 6.3 : ** Solutions of Questions on Page Number : **121**

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**Exercise 6.4 : ** Solutions of Questions on Page Number : **126**

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**Exercise 6.5 : ** Solutions of Questions on Page Number : **130**

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Q1 :
**
**

In ΔPQR, D is the mid-point of .

is __________.

PD is __________.

Is QM = MR?

**Answer :**

(i) Altitude

(ii) Median

(iii) No

Answer needs Correction? Click Here

Q2 :
**
**

Draw rough sketches for the following:

(a) In ΔABC, BE is a median.

(b) In ΔPQR, PQ and PR are altitudes of the triangle.

(c) In ΔXYZ, YL is an altitude in the exterior of the triangle.

**Answer :**

(a)

(b)

(c)

Here, it can be observed that for ΔXYZ, YL is an altitude drawn exterior to side XZ which is extended up to point L.

Answer needs Correction? Click Here

Q3 :
**
**

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

**Answer :**

Q1 :
**
**

Find the value of the unknown exterior angle *x* in the
following diagrams:

**Answer :**

Q2 :
**
**

Find the value of the unknown interior angle *x* in the
following figures:

**Answer :**

Q1 :
**
**

Find the value of the unknown *x* in the following diagrams:

**Answer :**

Q2 :
**
**

Find the value of the unknowns *x* and *y* in the
following diagrams:

**Answer :**

Q1 :
**
**

Is it possible to have a triangle with the following sides?

(i) 2 cm, 3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm

(iii) 6 cm, 3 cm, 2 cm

**Answer :**

Q2 :
**
**

Take any point O in the interior of a triangle PQR. Is

(i) OP + OQ > PQ?

(ii) OQ + OR > QR?

(iii) OR + OP > RP?

**Answer :**

Q3 :
**
**

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

**Answer :**

Q4 :
**
**

ABCD is quadrilateral.

Is AB + BC + CD + DA >AC + BD?

**Answer :**

Q5 :
**
**

ABCD is quadrilateral.

Is AB + BC + CD + DA < 2 (AC + BD)?

**Answer :**

Q6 :
**
**

The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?

**Answer :**

Q1 :
**
**

PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.

**Answer :**

Q2 :
**
**

ABC is a triangle right angled at C. If AB = 25 cm and AC = 7 cm, find BC.

**Answer :**

Q3 :
**
**

A 15 m long ladder reached a window 12 m high from the ground on
placing it against a wall at a distance *a*. Find the
distance of the foot of the ladder from the wall.

**Answer :**

Q4 :
**
**

Which of the following can be the sides of a right triangle?

(i) 2.5 cm, 6.5 cm, 6 cm

(ii) 2 cm, 2 cm, 5 cm

(iii) 1.5 cm, 2 cm, 2.5 cm

In the case of right-angled triangles, identify the right angles.

**Answer :**

Q5 :
**
**

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.

**Answer :**

Q6 :
**
**

Angles Q and R of a ΔPQR are 25° and 65°.

Write which of the following is true:

(i) PQ^{2} + QR^{2}= RP^{2}

(ii) PQ^{2} + RP^{2}= QR^{2}

(iii) RP^{2} + QR^{2}= PQ^{2}

**Answer :**

Q7 :
**
**

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

**Answer :**

Q8 :
**
**

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

**Answer :**

Maths : CBSE ** NCERT ** Exercise Solutions for Class 7th for ** The Triangle and its Properties ** ( Exercise 6.1, 6.2, 6.3, 6.4, 6.5 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Chapter 2 - Fractions and Decimals Class 7
- Chapter 1 - Integers Class 7
- Chapter 4 - Simple Equations Class 7
- Chapter 5 - Lines and Angles Class 7
- Chapter 3 - Data Handling Class 7
- Chapter 9 - Rational Numbers Class 7
- Chapter 10 - Practical Geometry Class 7
- Chapter 11 - Perimeter and Area Class 7
- Chapter 12 - Algebraic Expressions Class 7

Exercise 6.1 |

Question 1 |

Question 2 |

Question 3 |

Exercise 6.2 |

Question 1 |

Question 2 |

Exercise 6.3 |

Question 1 |

Question 2 |

Exercise 6.4 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Exercise 6.5 |

Question 1 |

Question 2 |

Question 3 |

Question 4 |

Question 5 |

Question 6 |

Question 7 |

Question 8 |