List of top Mathematics Questions on Properties of Triangles asked in Maharashtra Class X Board

In the following figure $\triangle$ ABC, B-D-C and BD = 7, BC = 20, then find $\frac{A(\triangle ABD)}{A(\triangle ABC)}$.

In $ \triangle ABC $, ray $ BD $ bisects $ \angle ABC $, $ A - D - C $, and $ \text{seg } DE \parallel \text{side } BC $. If $ A - E - B $, then for showing $ \frac{AB}{BC} = \frac{AE}{EB} $, complete the following activity:

$ ABCD $ is a trapezium, $ AB \parallel CD $, and the diagonals of the trapezium intersect at point $ P $. Write the answers to the following questions:
[(a)] Draw the figure using the given information.
[(b)] Write any one pair of alternate angles and opposite angles.
[(c)] Write the names of similar triangles with a test of similarity.

Segment $ PM $ is a median of $ \triangle PQR $, $ PM = 9 $, and $ PQ^2 + PR^2 = 290 $. Find $ QR $.

Prove that, "If a line parallel to a side of a triangle intersects the remaining sides in two distinct points, then the line divides the sides in the same proportion."

Find the length of the hypotenuse of a right-angled triangle if the remaining sides are $ 9 \, \text{cm} $ and $ 12 \, \text{cm} $.

Out of the dates given below, which date constitutes a Pythagorean triplet?

In $\triangle PQR$, seg $PM$ is a median. Angle bisectors of $\angle PMQ$ and $\angle PMR$ intersect sides $PQ$ and $PR$ in points $X$ and $Y$ respectively. Prove that $XY \parallel QR$.

In $\triangle RST$, $\angle S = 90^\circ$, $\angle T = 30^\circ$, and $RT = 12$ cm, then find $RS$.

If $a$, $b$, $c$ are sides of a triangle and $a^2 + b^2 = c^2$, name the type of triangle: