Altitude

Q. The point of intersection of all the three altitudes of a triangle is called the

1. orthocenter
2. incenter
3. centroid

Q.

An orthocenter is the intersection of three

1. angle bisectors in a triangle.

2. Altitudes in a triangle.

3. medians in a triangle.

4. perpendicular bisectors in a triangle.

Q.

Which of the following figures will have it's altitude outside triangle?

Q.

How many altitudes can a right angled triangle have?

1. 2

2. 4

3. 3

4. 1

Q.

If we draw a median AD in ∆ABC, are the altitudes of ∆ADB and ∆ADC equal in length? Justify. [2 MARKS]

Q.

The point of intersection of all the angle bisectors of the triangle is called _____.

1. incentre

2. centroid

3. orthocentre
4. circumcentre

Q.

Question 32

How many altitudes does a triangle have?

a) 1
b) 3
c) 6
d) 9

Q. If AD is the altitude of equilateral triangle ABC with side 6 cm, then value of BD is ___.

1. 3 cm
2. 2 cm
3. 12 cm
4. 6 cm

Q. For any triangle ABC, draw:
(i) All possible medians.
(ii) All possible altitudes. [4 MARKS]

Q.

If median, altitude, angel bisector and perpendicular bisector are the same line in the triangle then why are they given different names?

Q. How many altitudes a triangle can have?

1. One
2. Three
3. Four
4. Two

Q.

Number of altitudes in a triangle is:

1. 2

2. 3

3. 4

4. 5

Q. What is the difference between Median and Altitude ? [2 MARKS]

Q.

AM is a median of a triangle ABC.

Is AB + BC + CA > 2 AM?

(Consider the sides of triangles ΔABM and ΔAMC.)

Q. How many altitudes of a right-angled triangle are the same as its sides?

1. 1
2. 2
3. 3
4. None of the above

Q.

How many altitudes can a right angled triangle have?

1. 1

2. 2

3. 4

4. 3

Q.

Verify by drawing a diagram if the median and altitude of an isosceles triangle can be same.

Q.

Median and altitude of an isosceles triangle are one and the same.

1. True

2. False

Q. How many altitudes does a triangle have?

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

Q. How many altitudes of a right-angled triangle are the same as its sides?

1. 1
2. 2
3. 3
4. None of the above

Q. How many altitudes a triangle can have?

1. One
2. Three
3. Four
4. Two

Q.

It is given that $\angle$OBC is ${90}^{\circ }$.
Then, B must be the midpoint of CE.

1. False

2. True

Q. The perpendicular line segment from a vertex of a triangle to its opposite side is called .

1. a median
2. an altitude
3. a bisector

Q. Which of the following line segments represents an altitude?

1. AB
2. BE
3. CE
4. AE

Q. Draw a rough figure to illustrate the following statements:

(1) In ∆PQR, seg QN is an altitude.
(2) In ∆NPK, seg PS is a median.
(3) In ∆BCD, seg CM is a median and CE is an altitude.

Q. A triangle has altitude(s).

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

Q.

Median and altitude of an isosceles triangle are one and the same.

1. True

2. False

Q.

In the following right angled triangle, AB = BC, CD = BD. Find the measure of angle CDB.

1. 40^o

2. 90^o

3. 60^o

4. 30^o

Q.

AM is a median of ∆ABC. Prove that (AB + BC + CA) > 2AM.

Q. The longer side of a parallelogram is 54 cm and the corresponding altitude is 16 cm. If the altitude corresponding to the shorter side is 24 cm, find the length of the shorter side.