Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) State the SAS criterion for constructing a triangle.
SAS construction requires
Correct! SAS = Side-Angle-Side with the angle between the two given sides.
(2) Which triangle construction method uses two angles and one side?
The
Perfect! ASA = Angle-Side-Angle construction method.
(3) Name the instrument used to measure angles directly.
A
Excellent! Though in pure constructions, we avoid using protractors.
(4) Write the steps to construct a 90° angle using only a compass.
(5) Define locus of points equidistant from two fixed points.
The locus is the
Perfect! Every point on this locus is equidistant from both fixed points.
Short Answer Questions (2 Marks Each)
Note: Answer each question with complete construction steps and justifications and submit to subject teacher.
(1) Construct a triangle given base 5 cm, one adjacent angle 60°, and other adjacent side 6 cm.
(2) Construct a triangle similar to a given triangle with scale factor
(3) Construct a perpendicular bisector of a line segment and justify why it is perpendicular.
(4) Construct a triangle given base 6 cm, base angle 45°, and sum of other two sides 8 cm.
(5) Construct a triangle with sides 4 cm, 5 cm, and 6 cm using SSS method.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete construction steps and justifications and submit to subject teacher.
(1) Construct a triangle whose sides are 6 cm, 8 cm, and 10 cm, and then construct a similar triangle with scale factor 2/3.
(2) Construct a triangle with base 6 cm, base angle 60°, and difference of other two sides 2 cm.
(3) Construct a right triangle with base 5 cm and hypotenuse 13 cm.
(4) Construct a triangle ABC in which AB = 4 cm, BC = 5 cm, AC = 6 cm, and then construct another triangle similar to it with scale factor
(5) Construct a tangent to a circle of radius 4 cm from a point 7 cm away from its center.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) Constructing a triangle given two sides and included angle is:
(a) SAS method (b) SSS method (c) ASA method (d) RHS method
Correct! SAS = Side-Angle-Side with the included angle.
(2) Constructing a triangle given two angles and one side is:
(a) ASA method (b) SAS method (c) SSS method (d) AAA method
Correct! ASA = Angle-Side-Angle construction method.
(3) A perpendicular bisector always:
(a) Passes through midpoint (b) Is parallel to line (c) Divides line into unequal parts (d) Bisects an angle
Correct! Perpendicular bisector passes through midpoint at 90°.
(4) In constructing a tangent from an external point to a circle, which theorem is applied?
(a) Pythagoras theorem (b) Thales theorem (c) Midpoint theorem (d) Basic proportionality theorem
Correct! Thales theorem: angle in semicircle is 90°.
(5) The scale factor less than 1 gives:
(a) Smaller similar triangle (b) Bigger similar triangle (c) Equal triangle (d) No triangle
Correct! Scale factor < 1 reduces the size of the triangle.
(6) To construct a triangle when three sides are known, we use:
(a) SSS construction (b) SAS construction (c) ASA construction (d) RHS construction
Correct! SSS = Side-Side-Side construction for three known sides.
(7) The difference of two sides of a triangle is given in:
(a) Special construction problems (b) SSS construction (c) ASA construction (d) RHS construction
Correct! Sum or difference problems require special construction techniques.
(8) Constructing a tangent to a circle uses:
(a) Compass and ruler (b) Protractor only (c) Ruler only (d) Calculator
Correct! All geometric constructions use only compass and ruler.
(9) A right triangle can be constructed using:
(a) RHS condition (b) SSS condition (c) ASA condition (d) AAA condition
Correct! RHS = Right angle-Hypotenuse-Side for right triangles.
(10) The bisector of an angle divides the angle into:
(a) Two equal angles (b) Two complementary angles (c) Two supplementary angles (d) Unequal parts
Correct! Bisector divides an angle into two equal parts.
Construction Methods Challenge
Determine whether these statements are True or False: