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:
- 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?
- 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.