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Standard X

Mathematics

Perpendicular from Right Angle to Hypotenuse Divides the Triangle into Two Similar Triangles

A perpendicul...

Question

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.

True

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False

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Solution

The correct option is B
False

A perpendicular drawn from the vertex of the right angle of a right-angled triangle divides the triangle into two triangles similar to each other and also to the original triangle. If the perpendicular is drawn from one of the acute acute angles then the triangle is not divided into similar triangles.

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Similar questions

Q. In a right - angled triangle, the hypotenuse is

2 \sqrt{2}

times the perpendicular drawn from the opposite vertex, then the other acute angles of the triangle are

Q. When one acute angle of a triangle is equal to one acute angle of other triangle, and the triangles are right angles, do you think the triangles are similar?

State, true or false :
(i) Two similar polygons are necessarily congruent.
(ii) Two congruent polygons are necessarily similar.
(iii) All equiangular triangles are similar.
(iv) All isosceles triangles are similar.
(v) Two isosceles-right triangles are similar.
(vi) Two isosceles triangles are similar if an angle of one is congruent to the corresponding angle of the other.
(vii) The diagonals of a trapezium divide each other into proportional segments.

Q. In a right angled triangle, the hypotenuse is

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times the length of the perpendicular drawn from the opposite vertex on the hypotenuse then the acute angles of the triangle.

Q. Question 8
If in two right triangles, one of the acute angles of one triangle is equal to an acute of the other triangle. Can you say that two triangles will be similar? Why?

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