PRACTICAL GEOMETRY

1

How many medians are needed to find the centroid of a triangle?

A Two medians B One median C Three medians D All three medians

2

Anum is constructing a triangle with sides 9 cm, 12 cm, and 15 cm. What type of triangle is formed?

A Equilateral B Isosceles C Right-angled D Obtuse

3

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

4

How many medians can a triangle have?

A 3 B 1 C 2 D 6

5

Which tool is used to draw perpendicular bisectors in practical geometry?

A Compass and ruler B Protractor only C Set square only D Divider

6

What is the orthocenter of an obtuse triangle?

A Outside the triangle B Inside the triangle C On the triangle D At the midpoint of the longest side

7

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

8

Rizwan is constructing the perpendicular bisector of a line segment AB. The perpendicular bisector passes through which point?

A Point A B Point B C Midpoint of AB D Any point on AB

9

In a scalene triangle, the perpendicular bisectors:

A Meet at a point inside or outside B Always meet inside C Never meet D Always meet on the triangle

10

Fatima is constructing a triangle given two sides and the included angle (SAS). She draws the included angle first. What should she do next?

A Draw the third side B Mark the two given sides on the angle arms C Draw the altitude D Draw a perpendicular bisector

11

What is the median from a vertex to the opposite side?

A A segment joining the vertex to the midpoint of the opposite side B A perpendicular from the vertex to the opposite side C A line bisecting the angle at the vertex D A line joining the midpoints of two sides

12

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

13

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

14

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

15

Kashif is constructing a triangle with sides 5 cm, 5 cm, and 5 cm. What is the measure of each angle?

A 30° B 45° C 60° D 90°

16

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

17

What is the point equidistant from all sides of a triangle?

A Incenter B Circumcenter C Centroid D Orthocenter

18

Which of the following sets of angles can form a triangle?

A 40°, 60°, 80° B 30°, 60°, 100° C 50°, 50°, 50° D 90°, 45°, 55°

19

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

20

What is the centroid of a triangle?

A The point of intersection of the medians B The point of intersection of the altitudes C The point of intersection of perpendicular bisectors D The point of intersection of angle bisectors

21

Nimra is drawing the altitude from vertex A to side BC of triangle ABC. The altitude divides BC into segments of lengths 3 cm and 4 cm. If AB = 5 cm, what is AC?

A 4 cm B 5 cm C 6 cm D 7 cm

22

Mariam is constructing an isosceles triangle with base 6 cm and equal sides 5 cm. What is the height from the apex to the base?

A 3 cm B 4 cm C 5 cm D 6 cm

23

Adeel is constructing a triangle with sides 5 cm, 12 cm, and 13 cm. What type of triangle is formed?

A Equilateral B Isosceles C Right-angled D Obtuse

24

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

25

A triangle with sides 7 cm, 8 cm, and 15 cm:

A Cannot be constructed B Can be constructed with a right angle C Can be constructed as acute triangle D Can be constructed as obtuse triangle