GEOMETRY AND POLYGONS + PRACTICAL GEOMETRY

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

In an equilateral triangle, the altitude and median from the same vertex are:

A The same line B Perpendicular lines C Parallel lines D Different lines

3

What is the sum of interior angles of a pentagon?

A 360° B 540° C 720° D 900°

4

How do you construct the median of a triangle?

A Join vertex to midpoint of opposite side B Draw perpendicular from vertex to opposite side C Bisect the angle at the vertex D Join midpoints of two sides

5

What is the length of the median from vertex A in triangle ABC if the sides are AB = 6, AC = 8, and BC = 10?

A 5 B 7 C 6 D 4

6

The locus of points at a distance of 7 units from a point P is:

A A line 7 units long B A circle with radius 7 C A square with side 7 D A sphere of radius 7

7

If two polygons are similar, their corresponding angles are:

A Equal B Proportional C Supplementary D Complementary

8

Babar is constructing a triangle given two sides and a non-included angle (SSA). Why can this be ambiguous?

A It always gives one triangle B It may give two possible triangles C It never forms a triangle D It always gives a right triangle

9

What is the first step in constructing a triangle when given three sides?

A Draw the longest side as the base B Draw the shortest side as the base C Draw any side as the base D Draw an angle first

10

What is the orthocenter of an acute triangle?

A Inside the triangle B On the triangle C Outside the triangle D At the vertex

11

Jibran is constructing a triangle with angles 120°, 30°, and 30°. What type of triangle is formed?

A Acute-angled B Right-angled C Obtuse-angled isosceles D Equilateral

12

Nashit is constructing a triangle with angles 45°, 45°, and 90°. What type of triangle is formed?

A Equilateral B Isosceles right-angled C Scalene right-angled D Obtuse

13

What is the perpendicular bisector of the hypotenuse in a right triangle?

A Passes through the circumcenter B Passes through the orthocenter C Passes through the centroid D Passes through the incenter

14

How many medians can a triangle have?

A 3 B 1 C 2 D 6

15

Arslan is constructing a right-angled triangle given hypotenuse 10 cm and one acute angle 30°. Which construction method is he using?

A SSS B SAS C ASA D RHS or ASA

16

Zara is drawing an altitude from vertex A to side BC of triangle ABC. What is the angle between the altitude and side BC?

A 45° B 60° C 90° D 180°

17

What is the altitude of a triangle in an obtuse triangle from an acute vertex?

A Falls outside the triangle B Falls inside the triangle C Falls on the opposite side D Coincides with a side

18

The altitude of a triangle is a line segment drawn from a vertex:

A Perpendicular to the opposite side B Parallel to the opposite side C Bisecting the opposite side D Bisecting the angle at the vertex

19

How many medians can a triangle have?

A 3 B 1 C 2 D 6

20

Ayesha is finding the point of concurrency of the altitudes of a triangle. What is this point called?

A Centroid B Circumcenter C Orthocenter D Incenter

21

Which of the following is used to draw the perpendicular bisector of a line segment?

A Compass arcs from both endpoints B Ruler alone C Protractor alone D Set square alone

22

What is the measure of each exterior angle of a regular hexagon?

A 30° B 45° C 60° D 90°

23

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

24

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

25

What is the distance from the vertex to the centroid compared to the median length?

A 2/3 of the median B 1/3 of the median C 1/2 of the median D 3/4 of the median