The Triangles and its properties Class 7 Worksheet Maths

Ans. C

Ans. (i) 2
(ii) Hypotenuse
(iii) Altitude or Perpendicular bisector
(iv) Median

Ans.  

Ans. 

In the given star-shaped figure, the angles at the vertices (∠A, ∠B, ∠C, ∠D, ∠E, ∠F) are formed by intersecting lines. The sum of the angles around a point in any polygon is 360°.

Thus, the value of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F is 360°.

Ans.

The height difference between the two poles is 14m - 8m = 6m. Using the Pythagorean theorem:

(Base)² + (Height Difference)² = (Distance Between Tops)²

Let the base be x. So,

x² + 6² = 10²

x² + 36 = 100

x² = 64, therefore x = 8m.

The distance between their feet is 8 meters.

Ans. 

Mohini walks 1200m east and then 500m north. This forms a right-angled triangle, where the horizontal distance is 1200m, and the vertical distance is 500m.

Using the Pythagorean theorem:

Distance² = (1200)² + (500)²

Distance² = 1440000 + 250000

Distance² = 1690000

Taking the square root:

Distance = √1690000 = 1300m

So, Mohini is 1300 meters away from her starting point.

Ans. (i) 
x = 70°  (Corresponding Angle)
70° +  40° + y = 180°

So, x = 180° - 110° = 70°.
Hence, x = 70° , y = 70°

(ii) 

x + 60° = 180° (Linear Pair)x = 180 - 60° x = 120°

y + 50°  = 120° (Exterior Angle Property)

So, y = 120° - 50° = 70°.

Thus, y = 70° and x = 120°.

(iii) x =50° + 30° = 80° (Exterior Angles Property)
In Triangle PQR, 30° + 45° + ∠Q = 180°  (Angle sum property)
∠Q =  180° - 75° = 105°
∠Q = 105°
In Triangle QSP,
80° +  45° + ∠SQP = 180° (Angle sum property)
125° + ∠SQP = 180°
∠SQP = 180° - 125° = 55°
50° + 55° + y = 180°
y = 180° - 105°  = 75° 
x =  80° , y = 75° 
(iv) x = 80° (Vertically Opposite angle) 
y + 50° + 80° = 180° (Angle sum property)
y = 180°  - 130° = 50° 
x = 80°, y = 50° 

Ans. (i)

Given angles: 3x°, 2x°, and x°.

Using the angle sum property of a triangle:
3x° + 2x° + x° = 180°6x° = 180°x = 180° / 6 = 30°

• x = 30°
• 3x = 90°
• 2x = 60°

(ii)

• Given angles: 50°, 50°, and x°.
• Using the angle sum property of a triangle:
  50° + 50° + x° = 180°
  x° + 100° = 180°
  x° = 100°
  x = 100° / 2 = 50°
  Therefore, the angles x = 50° 

(iii)

• Given angles: x°, 2x°, and a right angle (90°).
• Using the angle sum property of a triangle:
  x° + 2x° + 90° = 180°
  3x° = 90°
  x = 90° / 3 = 30°
• Therefore, the angles are:
  • x = 30°
  • 2x = 60°
    Thus, the values for each triangle are: x = 30°,  2x = 60°

(iv)

Given angles: 30°, 122°, and x°.

Using the angle sum property of a triangle:30° + 122° + x° = 180°

Simplifying:152° + x° = 180°

Now, subtract 152° from both sides:x° = 180° - 152° = 28°

Thus, the value of x is 28°

Ans. AD² =

Ans. (i) False
(ii) True
(iii) False
(iv) False