Class 10

Math

All topics

Triangles

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C. Prove that $AE_{2}+BD_{2}=AB_{2}+DE_{2}$.

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D is a point on side BC of $ΔABC$such that $AD=AC$(see Fig. 7.47).Show that $AB>AD$.

Two poles of heights $6$ m and $11$ m stand on aplane ground. If the distance between the feet of the poles is $12$ m, find the distance between their tops.

$ABC$ is a triangle in which altitudes $BE$ and $CF$ to sides $AC$ and $AB$ are equal (see Fig.). Show that(i) $△ABE≅△ACF$(ii) $AB=AC$, i.e., $ABC$ is an isosceles triangle.

The areas of the two similar triangles are in the ratio of the square of the corresponding medians.

ABC is a triangle. Locate a point in the interior of $ΔABC$which is equidistant from all the vertices of $ΔABC$

Give two different examples of pair of(i) similar figures. (ii) non-similar figures.

In an equilateral triangle, prove that three times the square of one side is equal to four times the square of one of its altitudes.

In figure D is a point on side BC of a $ΔABC$such that $CDBD =ACAB $. Prove that AD is the bisector of $∠BAC$.