# The Triangle and its Properties – Class 7.

**Chapter 6 of NCERT/CBSE Class 7 Maths is about the Triangle and its properties. Here in this lesson, you can find practice problems for this chapter.**

**CBSE CLASS 7 MATHEMATICSThe Triangle and its Properties – Chapter 6Answer the following:**

- One of the angles of a triangle is 80 degree and the other two angles are equal. Find the measure of each of the equal angles.
- Two angles of a triangle are 30 degree and 80 degree. Find the third angle.
- Classify the following triangle on the basis of sides:

a) 4 cm, 5 cm, 6 cm

b) 3.5 cm, 3.5 cm, 5 cm

c) 6 cm, 6cm, 6cm - Is it possible to have a triangle with the following sides?

a) 2.5 cm, 3.5 cm, 6.5 cm

b) 3.5 cm, 4.5 cm, 7cm - One of the equal angles of an isosceles triangle is 70 degree. Find the third angle.
- Write the six elements of triangle ABC.
- Classify the following triangles on the basis of angles.

a) Triangle ABC with angle B = 90 degree

b) Triangle XYZ with angles X = 30, Y = 70, Z = 80 degrees. - If the two angles of a triangle are 60 and 30.Find the measure of third angle.
- Determine whether the triangle whose lengths of sides are 3 cm, 4cm, and 5cm is a right angled triangle.
- The two interior opposite angles of an exterior angle of a triangle are 50 degree 70 degree. Find the measure of the exterior angle?

**ANSWERS:**

- Given one of the angle is 80 degree.

Let the other two angles be x.

By angle sum property of triangles, sum of three angles = 180 degree

Therefore, x + x + 80 = 180

2x + 80 = 180

2x = 180 – 80 = 100

x = 100/2 = 50.

So the measure of equal angles is 50 degree. - Given two angles are 30 degree and 80 degree.

Let the third angle be x.

By angle sum property, we know that x + 30 + 80 = 180

x + 110 = 180

x = 180 – 110 = 70 degree

So the measure of third angle is 70 degree. - a) Scalene triangle

b) Isosceles triangle

c) Equilateral triangle - a) Suppose such a triangle is possible.

Then the sum of the lengths of any 2 sides would be greater than the length of the third side.

Here 2.5 + 3.5 = 6 < 6.5 2.5 + 6.5 = 9 > 3.5

3.5 + 6.5 = 10> 2.5

Therefore, this triangle is not possible.

b) Here 3.5 +4.5 = 8 > 7

3.5 + 7 = 10.5 > 4.5

4.5 + 7 = 11.5 > 3.5

Therefore, this triangle is possible. - Given triangle is an Isosceles triangle and its measure is 70 degree.

Let the other angle be x.

By angle sum property of triangles, x + 70 + 70 = 180

x + 140 = 180

x = 180 – 140 = 40 degree

Therefore, the measure of third angle is 40 degree. - Three sides are AB, BC, and AC

Three angles are <A, <B, <C. - a) Right angled triangle

b) Acute angled triangle - Given the measures of two angles are 60 and 30 degree.

By angle sum property of triangles, measure of third angle = 180 – (60 + 30)

= 180 – 90 = 90 degree - In any right angled triangle, the hypotenuse happens to be the longest side. In this question, the side with length 5 cm is the hypotenuse.

Also this triangle satisfies Pythagoras property, so the triangle is right angled. - By exterior angle sum property, we know that an exterior angle of a triangle is equal to the sum of its interior opposite angles.

Measure of exterior angle = 50 + 70 = 120 degree.