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\ 15-Nov-2024 Surender Prajapati Proof-5 Reader’s Sign _______________________ Date __________

Chapter assessment
A. Choose the correct option.
1. Which of the following angles cannot be constructed using a ruler and compasses?
(a) 75° (b) 15° (c) 135° (d) 85°

2. The instrument to draw a circle is
(a) Ruler (b) Protractor (c) Divider (d) Compasses
3. How many perpendiculars can be drawn on a line from a point outside of a given line?
(a) 0 (b) 1 (c) 2 (d) Many
4. Which of the given cases does not prove correct to construct a triangle?

(a) 7.8 cm, 4 cm, 5 cm (b) 3 cm, 7 cm, 5 cm (c) 5 cm, 5 cm, 12 cm (d) 5.5 cm, 11.5 cm, 6.5 cm
5. A triangle can be constructed by taking two of its angles as:
(a) 110°, 40° (b) 70°, 115° (c) 135°, 45° (d) 90°, 90
6. DABC can be constructed with AC = 8 cm, ∠A = 60°, ∠C = 50° using criterion .............. .
(a) ASA (b) SAS (c) SSS (d) RHS
B. Assertion and Reason Type Questions.
In the following question, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct choice as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of
Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
1. Assertion (A): When to construct a right-angled triangle, we must know the length of two sides.
Reason (R): When to construct a right-angled triangle, we must know the only hypotenuse.
2. Assertion (A): A triangle can be constructed by taking its base angles 110° and 40°, and base 6 cm.
Reason (R): If the measure of two base angles and the length of the side included within the angles
are given, then the triangle can be constructed by the SAS criterion.
C. Answer the following.
1. Draw a line segment XY of length 5.6 cm. Mark a point O outside this line segment. Draw a line
through O perpendicular to XY using a ruler and compasses.
2. Draw a line segment PQ of length 14 cm. Using compasses, divide it into four equal parts. Verify by
actual measurement.
3. With AB of length 8.2 cm as diameter, draw a circle.
4. Draw a line segment PQ of length 6.8 cm and draw a line perpendicular from point O outside the
line segment PQ by using a ruler and compasses.
5. Draw an angle of measure 154° and divide it into four equal parts.
6. Draw ∠XOY = 120° with the help of a protractor. Draw a line segment PQ = 5.4 cm, and construct an
angle equal to ∠XOY with a ruler and a pair of compasses.

7. Draw a semi-circle of radius 2.8 cm.
8. Construct a line segment AB of length 8.4 cm. From this, cut off AC of length 3.6 cm. Measure the
length of BC.
9. Construct an equilateral triangle DPQR in which PQ = 8 cm. Draw the perpendicular bisector of QR.

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