**NCERT Class 9 Maths Lab Manual – Verify that in a Triangle, Longer Side has the Greater Angle**

**OBJECTIVE**

To verify experimentally that in a triangle, the longer side has the greater angle opposite to it.

**Materials Required**

- Cardboard
- Coloured glazed papers
- White paper
- Tracing paper
- Scissors
- Geometry box
- Sketch pens
- Adhesive

**Prerequisite Knowledge**

Concept of triangle and its properties.

**Theory**

For concept of triangle and its properties refer to Activity 12.

**Procedure**

- Take a cardboard of suitable size and by using adhesive, paste a white paper on it.
- Cut out a ΔABC from a glazed paper and by using adhesive, paste it on cardboard, (see Fig. 15.1)

- Measure the lengths of all the three sides of ΔABC and identify that which of them is longest.
- All the three angles of a triangle are to be marked, (see Fig. 15.2)

- Using a tracing paper, make the cut out of the angle opposite to the longest side SC, i.e. ∠A. (see Fig. 15.3)

- Compare the cut out of the angle with remaining angles. (see Fig. 15.4)

**Demonstration**

We came to know that ∠A > ∠B and ∠A > ∠C , BC > AC,

So, we get since ∠A > ∠B

Also, BC > AB, since ∠A > ∠C

Thus, we observe that the angle belongs to longer side is greater than the angle opposite to other side.

**Observation**

Length of side AB = ……….. , Length of side BC = ………. , Length of side CA = ………… ,

Measure of the angle opposite to the longest side = …………. ,

Measure of the other two angles = …………… and ………. ,

The angle opposite to the …………. side ……….. is than either of the other two angles.

**Result**

We have verified experimentally that in a triangle, the longest side has the greater angle opposite to it.

**Application**

The result can be useful in different geometrical problems.

**Viva Voce**

**Question 1:**

In the right angled triangle, which one is the longest side?

**Answer:**

Hypotenuse

**Question 2:**

Does sum of any two sides of a triangle is always smaller than the third side?

**Answer:**

No, because the sum of any two sides of a triangle is always greater than the third side.

**Question 3:**

Is it possible to draw a triangle having sides 7 cm, 3 cm and 10 cm?

**Answer:**

No, because the sum of any two sides of a triangle is always greater than the third side.

**Question 4:**

Which type of triangle, have any two sides equal?

**Answer:**

Isosceles triangle

**Question 5:**

Which type of triangle, have all sides equal?

**Answer:**

Equilateral triangle

**Question 6:**

Does the longer side has the smaller angle opposite to it in a triangle?

**Answer:**

No, the longer side has the greater angle opposite to it in a triangle.

**Question 7:**

If in ΔABC, ∠A > ∠B, then what can you say about the opposite sides of ∠A and ∠B?

**Answer:**

BC > AC, because ∠A is greater than ∠B, so side opposite to ∠A will also be greater than the side opposite to ∠B.

**Question 8:**

Which type of triangle, have all sides unequal?

**Answer:**

Scalene triangle

**Suggested Activity**

Verify experimentally the relation between unequal sides of a triangle and the angles opposite to them.

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