1 If two similar solids have side lengths in ratio 1:4, what is the ratio of their volumes? A 1:4 B 1:16 C 1:64 D 1:8
2 If two similar triangles have areas in ratio 1:9, what is the ratio of their corresponding sides? A 1:3 B 1:9 C 1:81 D 3:1
3 Can a triangle be constructed if the sum of two sides is equal to the third side? A No, it forms a degenerate triangle B Yes, a unique triangle is formed C Yes, two triangles are formed D Sometimes, depending on the angles
5 In a triangle, if the altitude from the vertex is also the median, the triangle is: A Isosceles B Scalene C Equilateral D Right-angled
6 Can a triangle be constructed if two sides and the included angle are given? A Yes, by SAS criterion B Yes, but only one triangle is possible C No, not sufficient information D Yes, if the angle is obtuse
7 What is the locus of points that are at a distance less than 5 units from a fixed point? A Circle of radius 5 B Interior of a circle of radius 5 C Line segment D Square
8 The locus of points equidistant from the sides of an angle is the: A Perpendicular bisector B Angle bisector C Circle D Line segment
9 The medians of a triangle are concurrent at a point that divides each median in the ratio: A 2:1 from the vertex B 1:1 C 3:1 from the vertex D 1:2 from the vertex
10 If two polygons are similar, their corresponding angles are: A Equal B Proportional C Supplementary D Complementary
11 Which of the following cannot be constructed as a triangle? A 3 cm, 4 cm, 8 cm B 5 cm, 6 cm, 7 cm C 4 cm, 5 cm, 6 cm D 6 cm, 8 cm, 10 cm
12 In a right triangle, the altitude from the right-angle vertex to the hypotenuse: A Falls inside the triangle B Falls outside the triangle C Is the same as the hypotenuse D Is one of the legs
13 If two similar figures have side length ratio 5:2, what is the ratio of their volumes? A 25:4 B 125:8 C 5:2 D 10:4
14 If the ratio of volumes of two similar spheres is 1:8, what is the ratio of their radii? A 1:2 B 1:4 C 1:8 D 1:16
15 What is the circumcenter of a right triangle? A The midpoint of the hypotenuse B The right-angle vertex C Inside the triangle D Outside the triangle
16 What is the orthocenter of an acute triangle? A Inside the triangle B On the triangle C Outside the triangle D At the vertex
17 Which of the following conditions is sufficient to construct a unique triangle? A Three sides (SSS) B Two angles and a non-included side C Two sides and a non-included angle D Three angles
18 How do you construct an altitude from a vertex of a triangle? A Draw a perpendicular from the vertex to the opposite side B Draw a line from the vertex to the midpoint of opposite side C Draw a line bisecting the angle at the vertex D Draw a line parallel to the base
19 What is the incenter of a triangle? A Point of intersection of angle bisectors B Point of intersection of medians C Point of intersection of altitudes D Point of intersection of perpendicular bisectors