List of top Mathematics Questions on Triangles asked in Bihar Board X

ABC is an isosceles right triangle with C as right angle. Prove that \(AB^2 = 2AC^2\).
In any \(\triangle ABC\), \(\angle A = 90^\circ\), BC = 13 cm, AB = 12 cm; then the value of AC is
In \(\triangle DEF\) and \(\triangle PQR\) it is given that \(\angle D = \angle Q\) and \(\angle R = \angle E\), then which of the following is correct?
If one side of an equilateral triangle is \( a \), then its height is:
In triangle \( ABC \), \( DE \parallel BC \) such that
\[ \frac{AD}{DB} = \frac{4}{x - 4} \quad \text{and} \quad \frac{AE}{EC} = \frac{8}{3x - 19}, \] then the value of \( x \) is:
In \( \triangle ABC \) and \( \triangle PQR \), the area of \( \triangle ABC \) is to the area of \( \triangle PQR \) as \( 49:16 \), then the ratio of their corresponding sides is:
In \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \). If \( AB = 4 \, \text{cm} \), \( AC = 6 \, \text{cm} \), and \( BD = 2 \, \text{cm} \), then the value of \( DC \) is:
If the ratio of areas of two equilateral triangles is 9:4, then the ratio of their perimeters is:
In \( \triangle ABC \) and \( \triangle DEF \), \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = \frac{5}{7} \), then the ratio of the areas of \( \triangle ABC \) and \( \triangle DEF \) is:
If the ratio of corresponding sides of two similar triangles is 5:6, then the ratio of their perimeters is
In \( \triangle ABC \), \( AB = 6\sqrt{3} \, \text{cm}, AC = 12 \, \text{cm}, \) and \( BC = 6 \, \text{cm} \), then \( \angle B \) is
If one side of an equilateral triangle \( ABC \) is 12 cm and one side of equilateral triangle \( DEF \) is 6 cm, then the ratio of areas of \( \frac{\triangle ABC}{\triangle DEF} \) is:
If \( \triangle ABC \) and \( \triangle PQR \) are similar triangles in which \( AD \) is perpendicular from vertex \( A \) to \( BC \) and \( PT \) is perpendicular from vertex \( P \) to \( QR \), \( AD = 9 \, \text{cm} \) and \( PT = 7 \, \text{cm} \), then the ratio of areas of triangle \( \triangle AB \) and triangle \( \triangle PQR \) is
If in \( \triangle ABC \), \( AD \) is the bisector of \( \angle BAC \) and \( AB = \frac{1}{10} \, \text{cm}, AC = 14 \, \text{cm}, BC = 6 \, \text{cm} \), then the value of \( DC \) is
In \( \triangle ABC \), \( DE \parallel BC \) such that \( \frac{AD}{DB} = \frac{3}{5} \). If \( AC = 5.6 \, \text{cm} \), then \( AE \)= ?
In triangle \( \triangle PQR \), two points \( S \) and \( T \) are on sides \( PQ \) and \( PR \) such that \( \frac{PS}{SQ} = \frac{PT}{TR} \) and \( \angle PST = \angle PRQ \). Prove that \( \triangle PQR \) is an isosceles triangle.
In \( \triangle ABC \), \( \angle C = 90^\circ \) and \( P, Q \) are midpoints of \( CA \) and \( CB \) respectively. Prove that \( 4AQ^2 = 4AC^2 + BC^2 \).
In \( \triangle ABC \), \( AD \) is the bisector of \( \angle ABC \), \( AB = 4 \, \text{cm} \), \( AC = 6 \, \text{cm} \), and \( BD = 2 \, \text{cm} \). Find the value of \( DC \).
In triangle ABC, DE || BC such that \(\frac{AD}{DB} = \frac{4}{x-4}\) and \(\frac{AE}{EC} = \frac{8}{3x-19}\), then the value of x is:
If \( \triangle ABC \) has \( AB = 13 \) cm, \( BC = 12 \) cm, and \( AC = 5 \) cm, then \( \angle C \) is:
If the ratio of areas of two equilateral triangles is \( 9:4 \), then the ratio of their perimeters is:
If \( \triangle ABC \sim \triangle DEF \) and \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = \frac{5}{7} \), then the ratio of the areas of \( \triangle ABC \) and \( \triangle DEF \) is:
If one side of an equilateral triangle is \( a \), then its height is:
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
Construct a triangle with sides 4 cm, 5 cm, and 6 cm and then construct another triangle similar to it whose sides are \( \frac{2}{3} \) of the corresponding sides of the first triangle.