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 MATHEMATICS
The Triangle and its Properties – Chapter 6
Answer the following:

1. 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.
2. Two angles of a triangle are 30 degree and 80 degree. Find the third angle.
3. 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
4. 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
5. One of the equal angles of an isosceles triangle is 70 degree. Find the third angle.
6. Write the six elements of triangle ABC.
7. 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.
8. If the two angles of a triangle are 60 and 30.Find the measure of third angle.
9. Determine whether the triangle whose lengths of sides are 3 cm, 4cm, and 5cm is a right angled triangle.
10. 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:

1. 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.
2. 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.
3. a) Scalene triangle
   b) Isosceles triangle
   c) Equilateral triangle
4. 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.
5. 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.
6. Three sides are AB, BC, and AC
   Three angles are <A, <B, <C.
7. a) Right angled triangle
   b) Acute angled triangle
8. 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
9. 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.
10. 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.