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Standard VIII

Mathematics

Altitutes and Orthocentre

In which tria...

Question

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

Right angled triangle

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Obtuse angled triangle

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Acute angled triangle

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Equilateral triangle

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Solution

The correct option is A Right angled triangle
Right angled triangle JKL
The altitudes JK and KL and KM meet at vertex K, which is the orthocentre.

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Similar questions

Q. Orthocentre of an acute-angled triangle always lies _____ the triangle.

Q. If

O, G, H

be the circumcenter, centroid & orthocentre of triangle

A B C

, then

O, G, H

are collinear &

G

divide

O H

in the ratio

1 : 2

. In an equilateral triangle, these points coincide and in right-angled

△ A B C

orthocentre is the vertex at which triangle is a right angle.

For given two lines

a_{1} x + b_{1} y + c_{1} = 0

and

a_{2} x + b_{2} y + c_{2} = 0

the equations of bisectors of angles between these two lines are given by

\frac{a_{1} x + b_{1} y + c}{\sqrt{a_{1}^{2} + b_{1}^{2}}} = \pm \frac{a_{2} x + b_{2} y + c_{2}}{\sqrt{a_{2}^{2} + b_{2}^{2}}}

for the + ve sign we get the equation of bisector of angle in which origin lies. Also

a_{1} b_{2} + b_{1} b_{2} > 0

, then origin lies in obtuse angle and for

a_{1} a_{2} + b_{1} b_{2} < 0

, origin lies in acute angle

On the basis of above passage answer the following question:

One vertex of the equilateral triangle with centroid at the origin & one side as

x + y - 2 = 0

Given that in a triangle ABC, AB = 5.5 cm, BC = 5.5 cm, AC = 6 cm and $∠ A B C = 120^{\circ}$ . The given triangle is a/an ___ based on its sides and a/an ___ based on its angles.

Q. Assertion (

A

P (3, 5, 4)

Q (5, 7, 5)

R (6, 5, 7)

are vertices of a triangle whose orthocentre is

(5, 7, 5)

.
Reason ( R): In a right-angled triangle the right-angled vertex is orthocentre:

A perpendicular drawn from the vertex of one of the acute angles of a right angled triangle divides the triangle into two triangles similar to each other.

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

The correct option is A Right angled triangle Right angled triangle JKL The altitudes JK and KL and KM meet at vertex K, which is the orthocentre.

The correct option is A Right angled triangle
Right angled triangle JKL
The altitudes JK and KL and KM meet at vertex K, which is the orthocentre.