We will discuss here about the properties of triangle.

**Property 1:** Relation
between the measures of three angles of triangle

Draw three triangles on your not book. Name them as ∆PQR, ∆ABC and ∆LMN. With the help of protector measure all the angles the angles and find them: In ∆ABC ∠ABC + ∠BCA + ∠CAB = 180°
In ∆PQR ∠PQR + ∠QRP + ∠RPQ = 180° In ∆LMN ∠LMN + ∠MNL + ∠NLM = 180° |

Here, we observe that in each case, the sum of the measures of three angles of a triangle is 180°.

Hence, the sum of the three angles of a triangle is equals to 180°.

**Note:** If two angles of a triangle are given, we can easily find out its third angle.

**For Example:** **1.** In a right triangle, if one angle is 50°, find its third angle.

Solution:

∆ PQR is a right triangle, that is, one angle is right angle.

Given, ∠PQR = 90°

∠QPR = 50°

Therefore, ∠QRP = 180° - (∠Q + ∠ P)

= 180° - (90° + 50°)

= 180° - 140°

∠R = 40°

**Property 2: **Relation between lengths of the side

Draw a ∆ABC. Measure the length of its three sides. Let the lengths of the three sides be AB = 5 cm, BC = 7 cm, AC = 8 cm. Now add the lengths of any two sides compare this sum with the lengths of the third side.

(i) AB + BC = 5 cm + 7 cm = 12 cm

Since 12 cm > 8 cm

Therefore, (AB + BC) > AC

(ii) BC + CA = 7 cm + 8 cm = 15 cm

Since 15 cm > 5 cm

Therefore, (BC + CA) > AB

(iii) CA + AB = 8 cm + 5 cm = 13 cm

Since 13 cm > 7 cm

Therefore, (CA + AB) > BC

In the below figure we can see in each case, if we add up any two sides of the ∆, the sum is more than its third side.

Thus, we conclude that the sum of the length of any two sides of a triangle is greater than the length of the third side.

**For Example:** **1.** Is it possible to have a triangle whose sides are 5 cm, 6 cm and 4 cm?

Solution:

The lengths of the sides are 5 cm, 6 cm, 4 cm,

(a) 5 cm + 6 cm > 4 cm.

(b) 6 cm + 4 cm > 5 cm.

(c) 5 cm + 4 cm > 6cm.

Hence, a triangle with these sides is possible.

To Construct a Triangle whose Three Sides are given.

To Construct a Triangle when Two of its Sides and the included Angles are given.

To Construct a Triangle when Two of its Angles and the included Side are given.

To Construct a Right Triangle when its Hypotenuse and One Side are given.

Worksheet on Construction of Triangles.

**5th Grade Geometry Page**

**5th Grade Math Problems**

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