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## Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 4 Geometry Ex 4.3

Miscellaneous Practice Problems

Question 1.

What are the angles of an isosceles right-angled triangle?

Solution:

Since it is a right-angled triangle

One of the angles is 90°

The other two angles are equal because it is an isosceles triangle.

Other two angles must be 45° and 45°

Angles are 90°, 45°, 45°.

Question 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.

Solution:

(c) It is an obtuse isosceles triangle.

Question 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

Solution:

(c) an obtuse equilateral triangle

Question 4.

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

Solution:

In an isosceles triangle, any two sides are equal. Also, the two angles are equal.

Sum of three angles of a triangle = 180°

Given one angle = 124°

Sum of other two angles = 180° – 124° = 56°

Other angles are = \(\frac{56}{2}\) = 28°

28° and 28°.

Question 5.

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

Solution:

For a square all sides are equal and each angle is 90°.

∆ABC and ∆ADC are isosceles right-angled triangles.

Question 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?

Solution:

Here CA and DB are perpendicular to AB.

Yes CA and DB are parallel.

Construction:

(i) Drawn a line segment AB of length 6 cm.

(ii) Place the set square on the line in such a way that the vertex of its right angle coincides with B first and A next and one arm of the right angle coincides with the line AB.

(iii) Drawn lines DB and CA through B and A, the other arm of the right angle of the set square.

(iv) The line CA and DB are perpendicular to AB at A and B.

Challenge Problems

Question 7.

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

Solution:

No, a right-angled triangle cannot have more than one right angle.

Question 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.

Solution:

(a) It is true

In an equilateral triangle, all three sides are equal.

It can be an isosceles triangle also, which has two sides equal.

(b) But every isosceles triangle need not be an equilateral triangle.

Question 9.

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

Solution:

(i) Given one angle = 70°

Also, it is an isosceles triangle.

Another angle also can be 70°.

Sum of these two angles = 70° + 70° = 140°

We know that the sum of three angles in a triangle = 180°.

Third angle = 180° – 140° = 40°

One possibility is 70°, 70°, and 40°

(ii) Also if one angle is 70°

Sum of other two angles = 180° – 70° = 110°

Both are equal. They are \(\frac{110}{2}\) = 55°.

Another possibility is 70°, 55°, and 55°.

Question 10.

Which of the following can be the sides of an isosceles triangle?

(a) 6 cm, 3 cm, 3 cm

(b) 5 cm, 2 cm, 2 cm

(c) 6 cm, 6 cm, 7 cm

(d) 4 cm, 4 cm, 8 cm

Solution:

In a triangle sum of any two sides greater than the third side

(a), (b) and (d) cannot form a triangle.

(c) can be the sides of an isosceles triangle.

Question 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

Solution:

(a) ΔABC

(b) ΔABC, ΔAEF

(c) ΔAEB, ΔAED, ΔADF, ΔAFC, ΔABD, ΔADC, ΔABF, ΔAEC

(d) ΔABC, ΔAEF, ΔABF, ΔAEC

(e) ΔAEB, ΔAFC

(f) ΔADB, ΔADC, ΔADE, ΔADF

Question 12.

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

Solution:

Question 13.

Complete the following table.

Solution:

(i) Always acute angles

(ii) Acute angle

(iii) Obtuse angle