**NCERT Class 9 Maths Lab Manual – Verify Exterior Angle Property of a Triangle**

**OBJECTIVE**

To verify exterior angle property of a triangle.

**Materials Required**

- Cardboard sheet
- Adhesive
- Glazed papers
- White chart paper
- Geometry box
- Tracing paper
- Cutter

**Prerequisite Knowledge**

- Straight angle
- Exterior angle property of a triangle.

**Theory**

- For straight line refer to Activity 11.
- For exterior angle property of a triangle refer to Activity 12.

**Procedure**

- Take a cardboard sheet of suitable size and by using adhesive, paste a white chart paper on it.
- Cut out a ΔABC from a glazed paper and paste it on the cardboard, (see Fig. 13.1)

- Now, produce the side BC of ΔABC to the point D. (see Fig. 13.2)

- Cut out the pair of angles, ∠A and ∠B from the glazed paper by using a tracing paper, (see Fig. 13.3).

- Now, arrange the cut out angles as shown in Fig. 13.4.

**Demonstration**

From Fig. 13.4,

- ∠ACD is an exterior angle.
- ∠A and ∠B are its two interior opposite angles.
- The two cut out angles, ∠A and ∠B together completely cover ∠ACD. So, ∠ACD = ∠A + ∠B.

**Observation**

Measure of ∠A = ……… , and ∠B = ……… ,

Sum of (∠A + ∠B) = ……… , and measure of ∠ACD = ……… ,

Therefore, ∠ACD = ∠A + ∠B.

**Result**

We have verified the exterior angle property of a triangle.

**Application**

Many geometrical problems may be easily done, using this property of a triangle.

**Viva Voce**

**Question 1:**

What do you mean by the linear pair axiom?

**Answer:**

If a ray stands on a line, then the sum of the two adjacent angles so formed is 180° and vice-versa. This property is known as linear pair axiom.

**Question 2:**

What would be the measure of exterior angle for each vertex of equilateral triangle?

**Answer:**

120° (=60°+ 60°).

**Question 3:**

Does an exterior angle of a triangle is smaller than either of its interior opposite angles?

**Answer:**

No, an exterior angle of a triangle is greater than either of its opposite interior angles.

**Question 4:**

If the exterior angle of a triangle is 90°, then what would be the opposite interior angles, supplementary or complementary?

**Answer:**

Complementary.

**Question 5:**

How would you define an exterior angle property of a triangle?

**Answer:**

An exterior angle of a triangle is equal to sum of opposite interior angles.

**Question 6:**

If the sum of interior opposite angles of a triangle is 130°, then what would be the measure of its exterior angle?

**Answer:**

Sum of interior opposite angles = Exterior angle Exterior angle = 130°.

**Question 7:**

What is the angle form by straight line?

**Answer:**

The straight line always form a angle of 180°.

**Question 8:**

What is the condition of exterior angle of a triangle?

**Answer:**

The exterior angle of a triangle is equal to the sum of opposite interior angles.

**Question 9:**

What is the sum of exterior angles of a triangle?

**Answer:**

We know that the sum of exterior angles of a polygon is always 360°. The sum of exterior angles of a triangle is 360°.

**Suggested Activity**

To verify that the exterior angle of a triangle is greater than either of its opposite interior angles.

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