Concurrency of Altitudes of a Triangle

Q. If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

Q. In a/an triangle, all three sides are equal in length.

1. isosceles
2. equilateral
3. scalene

Q. If the altitude of the triangle are equal, then prove that it is the equilateral triangle

Q. A triangle in which one angle is ${90}^{\circ }$ is called a/an triangle.

1. acute angled
2. right angled
3. obtuse angled

Q. If one of the angle of a triangle is more than 90 degree , then it is called triangle.

1. an acute-angled
2. a right-angled
3. an obtuse-angled

Q.

If the three sides of a triangle are all different lengths, they form an isosceles triangle.

1. True

2. False

Q.

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

1. Similar triangles

2. Congruent triangles

3. Isoceles triangle

4. None of these

Q.

The sum of the three altitudes of a triangle is ..................... than its perimeter. [1 MARK]

Q. In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.

1. $\sqrt{4}5cm$
2. $\sqrt{2}7cm$
3. $\sqrt{3}0cm$
4. $\sqrt{2}5cm$

Q. All the sides of an equilateral triangle are___ .

Q.

If the altitude drawn from the vertices of ABC to the opposite sides are equal, prove that the triangle is equilateral.

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. 3
3. 6
4. 9

Q. 20. AD is an altitude of an equilateral triangle ABC . On AD as base , another equilateral triangle ADE is drawn . Prove that Ar(ΔABE):Ar(ΔABC)=3:4

Q.

How many acute angles does a right angled triangle have?

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

Q.

Name the types of triangle

$∆DEF$ such that $DE=EF=FD=6cm$.

Q.

Name the type of the given triangle.

$∆PQR$ with $PQ=QR=RP=5cm$

Q.

Incenter is the point of intersection of ___.

1. medians

2. angular bisectors

3. altitudes
4. perpendicular bisectors

Q.

Prove that the perimeter of a triangle is greater than the sum of its altitudes.

Q. An triangle has one obtuse angle and two acute angles.

1. acute-angle
2. obtuse-angle
3. reflex-angle
4. right-angle

Q. A triangle has altitude(s).

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. Match the special lines of a triangle given on the left with the name of their point of intersection.

1. centroid
2. incentre
3. orthocentre

Q.

In this figure the triangle shown is:

1. Right

2. Equilateral

3. Scalene

4. Isosceles

Q. To sir,
I have a doubt,
If a 4-sided polygon is known as Quadrilateral, then why don't we call triangle a trilateral?



From Arul Gupta

Q.

If triangle ABC is a isosceles triangle such that AB = AP is an altitude and AD bisects angle A.

Q. It is given that $\angle$AMC is ${90}^{\circ }$, which of the following is/are true regarding the figure given below?

1. M must be the midpoint of side BC.
2. $\Delta AMN$ is a right angled triangle.
3. AN is a median.
4. AM is an altitude.

Q.

The sum of the three altitudes of a triangle is _________ than its perimeter.

Q. A triangle has altitude(s).

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

Q.

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB, respectively. Then:

1. BE < CF

2. BE > CF

3. BE = 2CF

4. BE = CF

Q.

Triangle ABC is an equilateral triangle of side 10 cm. The perimeter of the triangle formed by joining its midpoints is ___ cm

1. 15

2. 16.5

3. 18.5

4. 33