Chapter 6: Triangles

Q31Written answer

Which of the following can be the length of the third side of a triangle whose two sides measure 18 cm and 14 cm?

(a) 4 cm (b) 3 cm (c) 5 cm (d) 32 cm

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Solution:-

(c) 5 cm

We know that,

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

So, 18 cm + 14 cm > 3^rd side

3^rd side < 32 cm

The difference of the lengths of any two sides of a triangle is always smaller than the length of the third side.

So, 18 – 14 < 3^rd side

3^rd side > 4 cm

Therefore, 5 cm is the length of the 3^rd side.

Q32Written answer

How many altitudes does a triangle have?

(a) 1 (b) 3 (c) 6 (d) 9

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Solution: –

(b) 3

The perpendicular line segment from a vertex of a triangle to its opposite side is called the altitude of the triangle. A triangle has 3 altitudes.

Q33Written answer

If we join a vertex to a point on opposite side which divides that side in the ratio 1:1, then what is the special name of that line segment?

(a) Median (b) Angle bisector (c) Altitude (d) Hypotenuse

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Solution:-

(a) Median

The line segment joining a vertex of a triangle to the mid point of its opposite side is called a median of the triangle.

Q34Written answer

The measures of ∠x and ∠y in Fig. 6.14 are respectively

(a) 30°, 60° (b) 40°, 40°

(c) 70°, 70° (d) 70°, 60°

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Solution:-

(d) 70^o, 60^o

We know that, the exterior angle is sum of interior opposite angles of triangle.

So, x + 50^o = 120^o

x = 120^o – 50^o

x = 70^o

We also know that, sum of angles of triangle are equal to 180^o.

So, 50^o + x + y = 180^o

50^o + 70^o + y = 180^o

120^o + y = 180^o

y = 180^o – 120^o

y = 60^o

Therefore, the measures of ∠x and ∠y is 70^o and 60^o, respectively.

Q35Written answer

If the length of two sides of a triangle are 6 cm and 10 cm, then the length of the third side can be

(a) 3 cm (b) 4 cm (c) 2 cm (d) 6 cm

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Solution: –

(d) 6 cm

We know that,

The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

So, 6 cm + 10 cm > 3^rd side

3^rd side < 16 cm

The difference of the lengths of any two sides of a triangle is always smaller than the length of the third side.

So, 10 – 6 < 3^rd side

3^rd side > 4 cm

Therefore, 6 cm is the length of the 3^rd side.

Q36Written answer

In a right-angled triangle ABC, if angle B = 90°, BC = 3 cm and AC = 5 cm, then the length of side AB is

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

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Solution: –

(b) 4 cm

From Pythagoras theorem.

AC² = AB² + BC²

5² = AB² + 3²

AB² = 25 – 9

AB² = 16

AB = √16

AB = 4 cm

Q37Written answer

In a right-angled triangle ABC, if angle B = 90°, then which of the following is true? (a) AB² = BC² + AC²

(b) AC² = AB² + BC²

(c) AB = BC + AC

(d) AC = AB + BC

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Solution:-

(b) AC² = AB² + BC² … [from Pythagoras theorem]

NCERT Exemplar Class 7 Maths Solutions Chapter 6 Image 13

Q38Written answer

Which of the following figures will have its altitude outside the triangle?

NCERT Exemplar Class 7 Maths Solutions Chapter 6 Image 14

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Solution:-

Figure (d) has its altitude outside the triangle

Q39Written answer

In Fig. 6.16, if AB || CD, then,

(a) ∠ 2 = ∠ 3 (b) ∠ 1 = ∠ 4

(c) ∠ 4 = ∠ 1 + ∠ 2 (d) ∠ 1 + ∠ 2 = ∠ 3 + ∠ 4

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Solution:-

(d) ∠ 1 + ∠ 2 = ∠ 3 + ∠ 4

As we know that, exterior angle is equal to the sum of opposite interior angles

Consider, Δ ABC

As BC is extended

∠A + ∠B = ∠3 + ∠4

Therefore, ∠1 + ∠2 = ∠3 + ∠4

Q40Written answer

In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD⊥BC. Then, ∠B is equal to

(a) 80^o (b) 20^o (c) 40^o (d) 30^o

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Solution: –

(c) 40^o

Consider the triangle ABC,

NCERT Exemplar Class 7 Maths Solutions Chapter 6 Image 16

From the figure, AD bisects ∠Α

Then, ∠BAD = 50^o

∠DAC = 50^o

So, AD⊥BC

∠ΑDC = 90^o

Consider the ∆ABD,

From the rule of exterior angle property of triangle,

∠ΑDC = ∠ΑBD + ∠BAD

90^o = ∠ΑBD + 50^o

∠ΑBD = 90^o – 50^o

= 40^o

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