6th Maths : Term 2 Unit 4 : Geometry : Exercise 4.3 : Miscellaneous Practice Problems, Challenge Problems , Text Book Back Exercises Questions with Answers, Solution

**Exercise
4.3**

__Miscellaneous
Practice Problems__

** **

**1. What are the angles of an isosceles
right angled triangle?**

45°, 45°, 90°

** **

**2. Which of the following correctly describes
the given triangle?**

(a) It is a right isosceles triangle.

(b) It is an acute isosceles triangle.

(c) It is an obtuse isosceles triangle.

(d) It is an obtuse scalene triangle.

Answer: **✓****(c) It is an obtuse
isosceles triangle.**

** **

**3. Which of the following is not possible
?**

(a) An obtuse isosceles triangle

(b) An acute isosceles triangle

(c) An obtuse equilateral triangle

(d) An acute equilateral triangle

Answer: **✓****(c) An obtuse
equilateral triangle **

** **

**4. If one angle of an isosceles triangle
is 124° , then find the other angles.**

One angle of an isosceles triangle = 124°

The sum of three angles of a triangle = 180°

The other two isosceles angles = 180° − 124° = 56°

One angle = 56 / 2 = 28°

**The other two angles are 28°, 28°.**

** **

**5. The diagram shows a square ABCD. If
the line segment joins A and C, then mention the type of triangles so formed.**

Both triangles are Isoceles
Right angled triangle.

** **

**6. Draw a line segment AB of length 6 cm. At each end of this line segment AB,
draw a line perpendicular to the line AB. Are these lines parallel?**

Yes. These two
perpendicular lines are parallel.

** **

__Challenge
Problems__

**7.
Is a triangle possible with the angles 90° , 90° and 0° Why? **

90°, 90°, 0°

A triangle can not be formed with the given angles. Because,
Atriangle can not have more than one right angle.

** **

**8.
Which of the following statements is true? Why? **

**(a)
Every equilateral triangle is an isosceles triangle.**

**(b)
Every isosceles triangle is an equilateral triangle.**

'a' is true. Because an
isosceles triangle need not have three equal sides.

** **

**9.
If one angle of an isosceles triangle is 70°, then find the possibilities for the
other two angles.**

One angle of an isosceles triangle = 70°

If the other angle also = 70°

The third angle = 180° − (70° + 70°)

= 180° − 140° = 40°

The other two angles are 70° and 40° (or)

One angle = 70°

The other two isosceles angles = (180° − 70°) = 110°

Two isosceles angles = 110°

So, one angle = 110 / 2 = 55°

The other two isosceles angles are 55° and 55°

So, the two angles 70°, 40° (or) may be, 55°, 55°..

**10.
Which of the following can be the sides of an isosceles triangle?**

**a) 6 cm,
3cm, 3cm **

**b) 5 cm,
2cm, 2cm **

**c) 6 cm,
6cm, 7cm **

**d) 4 cm,
4cm, 8cm **

**a) 6 cm, 3 cm, 3 cm**

The sum of two smaller sides = 3+3 = 6cm=6cm, the third side

The sum of two smaller sides is not greater than the third side.

So, a triangle can not be formed with the given sides.

**b) 5 cm, 2 cm, 2 cm**

The sum of two smaller sides=2 + 2 = 4 cm < 5 cm the third
side.

The sum of two smaller sides is lesser than the third side.

So, a triangle can not be formed with the given sides.

**c) 6 cm, 6 cm, 7 cm**

The sum of two smaller sides = 6 + 6 = 12 cm > 7 cm the third
side.

The sum of two smaller sides is greater than the third side.

So, a triangle can be formed with the given sides.

**d) 4 cm, 4 cm, 8 cm**

The sum of two smaller sides = 4 + 4 = 8 cm = 8 cm the third
side.

The sum of two smaller sides is not greater than the third side.

So, a triangle can not be formed with the given sides.

**11.
Study the given figure and identify the following triangles.**

**(a) equilateral triangle **

**(b) isosceles triangles**

**(c) scalene triangles **

**(d) acute triangles**

**(e) obtuse triangles **

**(f) right triangles**

**(a) Equilateral triangle **

Equilateral triangle ΔABC

**(b) Isosceles triangles **

Isosceles triangle Δ ABC, Δ AEF

(c) Scalene triangles

Scalene triangle Δ AEB, Δ AED, Δ ADF, Δ AFC, Δ ABD, Δ ADC, Δ ABF,
Δ AEC

**(d) Acute triangles**

Acute triangles Δ ABC, Δ AEF, Δ ABF, Δ AEC

**(e) Obtuse triangles**

Obtuse triangles Δ AEB, Δ AFC

**(f) Right triangles**

Right triangles Δ ADB, Δ ADC, Δ ADE, Δ ADF

**12.
Two sides of the triangle are given in the table. Find the third side of the triangle.**

**i) 7cm, 4 cm**

The sum of two smaller sides = 4 + 4 = 8 cm > 7 cm, the third
side

= 4 + 5 = 9 cm > 7 cm, the third side

= 4 + 6 = 10 cm > 7 cm, the third side

The third side is, 4 cm or 5 cm or 6 cm.

**ii) 8 cm, 8 cm**

The sum of two smaller sides = 5 + 8 = 13 cm >8 cm, the third
side

= 6 + 8 = 14 cm > 8 cm, the third side

= 7 + 8 = 15 cm > 8 cm, the third side

The third side is, 5 cm or 6 cm or 7 cm.

**iii) 7.5 cm, 3.5 cm**

The sum of two smaller sides = 3.5 + 4.5 = 8cm > 7.5 cm, the
third side

= 3.5 + 5 = 8.5 cm > 7.5 cm, the third side

= 3.5 + 6 = 9.5 cm > 7.5 cm, the third side

**The third side is 4.5 cm or 5 cm or 6 cm**

**iv. 10 cm, 14 cm**

The sum of two smaller sides = 10 + 5= 15 cm> 14 cm, the
third side

= 10 + 7 = 17cm > 14 cm, the third side

= 10 + 8 = 18 cm > 14 cm, the third side

**The third side is 5 cm or 7 cm or 8 cm**

** **

**13.
Complete the following table :**

** **

__ANSWERS: __

__Exercise 4.3 __

**1. 90°, 45° , 45°**

**2. c**

**3. c**

**4. 28°, 28°**

**5. Both are
Isosceles Right angled triangles**

**6. Yes **

**7. No, A triangle
cannot have more than one right angle**

**8. “a” is true,
because an isosceles triangle need not have three equal sides**

**9. 70°,40° or
55°,55° **

**10. c**

**11. a) ∆ABC **

**b) ∆ABC , ∆AEF**

**c) ∆AEB, ∆AED,
∆ADF, ∆AFC, ∆ABD, ∆ADC, ∆ABF, ∆AEC**

**d) ∆ABC, ∆AEF,
∆ABF, ∆AEC**

**e) ∆AEB, ∆AFC**

**f) ∆ADB, ∆ADC,
∆ADE, ∆ADF**

**12. (i) between 3
and 11 (ii) between 0 and 16 (iii) between 4 and 11 (iv) between 4 and 24**

**13. i .Always acute
angles**

** ii. Acute angle**

** iii. Obtuse angle**

** **

Tags : Questions with Answers, Solution | Geometry | Term 2 Chapter 4 | 6th Maths , 6th Maths : Term 2 Unit 4 : Geometry

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6th Maths : Term 2 Unit 4 : Geometry : Exercise 4.3 | Questions with Answers, Solution | Geometry | Term 2 Chapter 4 | 6th Maths

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