Altitude of a Triangle and Drawing Method

Q. A lamp post is situated at the middle point m of the side ac of a triangular plot abc with side bc=7m , ca=8m, ab=9m.lamp post substends an angle 15 degree at the point b .determine the height of lamp post.

Q. Draw an obtuse angled ∆ LMN. Draw its altitudes and denote the orthocentre by O.

Q. What is an Altitude?

1. Line segment drawn from vertex of triangle to opposite side of vertex.
2. Perpendicular line segment drawn from vertex of triangle to opposite side of vertex.
3. Line segment drawn from vertex of triangle to opposite side of vertex diving opposite side into two equal parts.
4. Line segment drawn from vertex of triangle dividing angle at that vertex into two equal parts.

Q.

Describe Right Angled Triangle

Q.

Orthocenter is the point of intersection of ___ of a triangle.

Q.

Sum of the three sides of a triangle is less than the sum of its three altitudes. True or False.

1. True

2. False

Q. The perimeter of a triangle is 36cm if the altitudes of the triangle are in the ratio of 1:2:3then find the lengths of the corresponding sides of the triangle

Q. In the given figure AD is altitude to triangle ABC, then which of the following is correct?

1. $\angle ADC$= ${90}^{\circ }$
2. BD = CD
3. AB = AC
4. $\angle ABD$= $\angle ACD$

Q. Answer the following: [2 MARKS]
(i) Angle opposite to CA in the $\Delta ABC$.
(ii) Side opposite to $\angle A$ in $\Delta AOD$.

Q. In an equilateral triangle ABC, AD is the median from vertex A to the side BC, the length of median is $\sqrt{2}7$ cm, then find the length of the equilateral triangle.

1. 6 cm
2. 9 cm
3. 3 cm
4. 7 cm

Q.

Justify the following statements with reasons:

(a) The sum of three sides of a triangle is more than the sum of its altitudes.

(b) The sum of any two sides of a triangle is greater than twice the median drawn to the third side.

(c) Difference of any two sides of triangle is less than the third side.

Q. If the side of a triangle measures 8cm, then the altitude divides the side into ___ cm and ____cm.

1. 2 cm and 6 cm
2. 6 cm and 2 cm
3. Cant be determined
4. 5 cm and 3 cm

Q.

QL, MR and PN, the three altitudes of the △PQR, are equal. △PQR is a/an _______ triangle.

1. Isosceles

2. Scalene

3. Equilateral

4. Right angled

Q.

The altitude of an equilateral triangle of side a to any of its other sides from the opposite vertex is

1. 

2. 

3. 

4. 

Q.

In which of the following triangles at least one of the altitudes and medians are same?

1. Isosceles Triangle

2. Scalene Triangle

3. Equilateral Triangle

4. None

Q.

The sides of a triangle are in the ratio 2 : 3: 4 and the longest side is 20 centimetres longer than the shortest side. Compute the length of each side.

Q.

The perimeter of a triangle is 10 metres and the lengths of two of its sides are and . What is the ratio of its sides?

Q.

Identify the type of triangle.

1. Equilateral triangle
2. Obtuse-angled triangle
3. Right-angled triangle
4. Acute-angled triangle

Q. There are 4 right triangles the ratio if perpendicular sides 3:4 in each. One more fact about each is given below. Find the lengths of the sides of each triangle.i) the different in the length of the perpendiclular sides is 24 meters.ii)the hypotension is 24mtrs. iii) the perimeter is 24 meters. IV the area is 24square metres

Q.

QL, MR and PN, the three altitudes of the △PQR, are equal. △PQR is a/an _______ triangle.

1. Isosceles

2. Scalene

3. Right angled

4. Equilateral

Q.

Can you name the altitude of the triangle given in the figure?

1. AE

2. AD

3. AF

4. AG

Q. Which triangle has its altitude outside the triangle?

1. Acute angled triangle
2. Equilateral triangle
3. Obtuse angled triangle
4. Right angled triangle

Q.

In which of the following triangles the altitude and medians are same?

1. Isosceles triangle
2. Scalene triangle
3. Equilateral triangle
4. Right angle triangle

Q.

In the figure given below, if lines PQ and RS intersect at point T, such that,
$\angle PRT={40}^{\circ }$, $\angle RPT={95}^{\circ }$ and $\angle TSQ={75}^{\circ }$, then find $2\angle SQT$.

1. ${80}^{\circ }$

2. ${120}^{\circ }$

3. ${150}^{\circ }$

4. ${90}^{\circ }$

Q.

For a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, RS = 5 cm, PS = 5.5 cm. What value must length of PR be below in cm?

__

Q. A triangle has altitude(s).

1. 1
2. 2
3. 3
4. infinite

Q. In which triangle does the orthocentre coincide with one of the vertex of the triangle?

1. Right angled triangle
2. Acute angled triangle
3. Equilateral triangle
4. Obtuse angled triangle

Q. An altitude has one end point at a vertex of the triangle and the other on the side which is opposite to that vertex , then how many altitudes does a triangle have?

1. 1
2. 9
3. 3
4. 6

Q.

In parallelogram ABCD, AB = 16 cm. The altitudes corresponding to sides AB and AD are respectively 8 cm and 10 cm. Then AD is equal to

1. 12.8 cm

2. 12.5 cm

3. 15 cm

4. 18 cm

Q. Find the next triangular number in the series 45, 55, …