Explain me this chapter
TRIANGLE AND ITS PROPERTIES... 7th standard
Answers
Answer:
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Answer:
Medians of a Triangle
Altitudes of a Triangle
Exterior Angle of a Triangle and Its Property
Angle Sum Property of a Triangle
Two Special Triangles: Equilateral and Isosceles
Sum of the Lengths of Two Sides of A Triangle
Right-Angled Triangles and Pythagoras Property
1. In Δ PQR, D is the mid-point of NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 1.
Solution:-
Altitude
An altitude has one end point at a vertex of the triangle and other on the line containing the opposite side.
(ii) PD is ___.
Solution:-
Median
A median connects a vertex of a triangle to the mid-point of the opposite side.
(iii) Is QM = MR?
Solution:-
No, QM ≠ MR because, D is the mid-point of QR.
2. Draw rough sketches for the following:
(a) In ΔABC, BE is a median.
Solution:-
A median connects a vertex of a triangle to the mid-point of the opposite side.
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 4
(b) In ΔPQR, PQ and PR are altitudes of the triangle.
Solution:-
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 5
An altitude has one end point at a vertex of the triangle and other on the line containing the opposite side.
(c) In ΔXYZ, YL is an altitude in the exterior of the triangle.
Solution:-
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 6
In the figure we may observe that for ΔXYZ, YL is an altitude drawn exteriorly to side XZ which is extended up to point L.
3. Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.
Solution:-
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 7
Draw a Line segment PS ⊥ BC. It is an altitude for this triangle. Here we observe that length of QS and SR is also same. So PS is also a median of this triangle.
Exercise 6.2 Page: 118
1. Find the value of the unknown exterior angle x in the following diagram:
(i)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 8
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= x = 50o + 70o
= x = 120o
(ii)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 9
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= x = 65o + 45o
= x = 110o
(iii)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 10
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= x = 30o + 40o
= x = 70o
(iv)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 11
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= x = 60o + 60o
= x = 120o
(v)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 12
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= x = 50o + 50o
= x = 100o
(vi)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 13
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= x = 30o + 60o
= x = 90o
2. Find the value of the unknown interior angle x in the following figures:
(i)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 14
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= x + 50o = 115o
By transposing 50o from LHS to RHS it becomes – 50o
= x = 115o – 50o
= x = 65o
(ii)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 15
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
= 70o + x = 100o
By transposing 70o from LHS to RHS it becomes – 70o
= x = 100o – 70o
= x = 30o
(iii)
NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and Its Properties Image 16
Solution:-
We Know That,
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
The given triangle is a right angled triangle. So the angle opposite to the x is 90o.
= x + 90o = 125o
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