**Exercise 17.1 **

** **

**Question 1: Draw an ∠BAC of measure 50 ^{o} such that AB = 5 cm and AC = 7 cm. Through C draw a line parallel to AB and through B draw a line parallel to AC, intersecting each other at D. Measure BD and CD**

**Solution 1:**

**Construction:**

^{o}such that AB = 5 cm and AC = 7 cm. and cut an arc through point C at an angle 50

^{o}.

^{o}

^{o}and Make a line passing through B and this arc and say this intersects the line drawn parallel to AB at D.

^{o}, since they are alternate angles. Thus, BD parallel to AC

**Question :2. Draw a line PQ. Draw another line parallel to PQ at a distance of 3 cm from it.**** **

**Solution 2:**

**Construction:**

^{o}and ∠QAE = 90

^{o}

**Question :3. Take any three non-collinear points A, B, C and draw ∠ABC. Through each vertex of the triangle, draw a line parallel to the opposite side.**** **

**Solution 3:**

**Construction:**

**Question :4. Draw two parallel lines at a distance of 5cm apart.**** **

**Solution 4:**

** **

**Construction:**

^{o}and ∠QAE = 90

^{o}

**Exercise 17.2**** **

**Question :1. Draw △ABC in which AB = 5.5 cm. BC = 6 cm and CA = 7 cm. Also, draw perpendicular bisector of side BC.**** **

**Solution 1:**

**Construction:**

**Question :2. Draw ∆PQR in which PQ = 3 cm, QR = 4 cm and RP = 5 cm. Also, draw the bisector of ∠Q**** **

**Solution 2:**

**Construction:**

^{o}.

**Question :3. Draw an equilateral triangle one of whose sides is of length 7 cm.**** **

**Solution 3:**

**Construction:**

**Question :4. Draw a triangle whose sides are of lengths 4 cm, 5 cm and 7 cm. Draw the perpendicular bisector of the largest side.**

**Solution 4:**

**Construction:**

**Question :5. Draw a triangle ABC with AB = 6 cm, BC = 7 cm and CA = 8 cm. Using ruler and compass alone, draw (i) the bisector AD of ∠A and (ii) perpendicular AL from A on BC. Measure LAD.**

**Solution 5:**

**Construction:**

^{o}angle.

**Question :6. Draw △DEF such that DE= DF= 4 cm and EF = 6 cm. Measure ∠E and ∠F.**

**Solution 6:**

**Construction:**

^{o}by measuring.

**Question :7. Draw any triangle ABC. Bisect side AB at D. Through D, draw a line parallel to BC, meeting AC in E. Measure AE and EC.**

**Solution 7:**

**Construction to bisect line AB:**

**Exercise 17.3**** **

**Question :1. Draw △ABC in which AB = 3 cm, BC = 5 cm and ∠B = 70 ^{o}.**

**Solution 1:**

**Construction:**

^{o}.

**Question :2. Draw △ABC in which ∠ A=70^{o}. AB = 4 cm and AC= 6 cm. Measure BC.**

**Solution 2:**

**Construction:**

^{o}.

**Question :3. Draw an isosceles triangle in which each of the equal sides is of length 3 cm and the angle between them is 45 ^{o}.**

**Solution 3:**

**Construction:**

^{o}drawing.

**Question :4. Draw △ABC in which ∠A = 120 ^{o}, AB = AC = 3 cm. Measure ∠B and ∠C.**

**Solution 4:**

**Construction:**

^{o}.

^{o}by measuring.

**Question :5. Draw △ABC in which ∠C = 90^{o} and AC = BC = 4 cm.**

**Solution 5:**

**Construction:**

**Question :6. Draw a triangle ABC in which BC = 4 cm, AB = 3 cm and ∠B = 45^{o}. Also, draw a perpendicular from A on BC.**

**Solution 6:**

**Construction:**

^{o}angle and cut an arc with a radius of 4 cm at this angle.

**Question :7. Draw a triangle ABC with AB = 3 cm, BC = 4 cm and ∠B = 60^{o}. Also, draw the bisector of angles C and A of the triangle, meeting in a point O. Measure ∠COA.**

**Solution 7:**

**Construction:**

^{o}.

^{o}.

**Exercise 17.4**** **

**Question :1. Construct ∆ABC in which BC = 4 cm, ∠B = 50 ^{o} and ∠C = 70^{o}.**

**Solution 1:**

**Construction:**

^{o}.

^{o}by placing Y on the same side of BC as X.

**Question :2. Draw ∆ABC in which BC = 8 cm, ∠B = 50 ^{o} and ∠A = 50^{o}.**

**Solution 2:**

**Construction:**

^{o}.

^{o}, with Y on the same side of BC as X.

**Question :3. Draw ∆ABC in which ∠Q = 80 ^{o}, ∠R = 55^{o} and QR = 4.5 cm. Draw the perpendicular bisector of side QR.**

**Solution 3:**

**Construction:**

^{o}.

**Question :4. Construct ∆ABC in which AB = 6.4 cm, ∠A = 45 ^{o} and ∠B = 60^{o}**

**Solution 4:**

**Construction:**

^{o}angle.

^{o}.

**Question :5. Draw ∆ABC in which AC = 6 cm, ∠A = 90 ^{o} and ∠B = 60^{o}**

**Solution 5:**

**Construction:**

^{o}angle.

^{o}.

^{o}.

**Exercise 17.5**** **

**Question :1. Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm.**** **

**Solution 1:**

**Construction:**

**Question :2. Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 2.5 cm.**** **

**Solution 2:**

**Construction:**

**Question :3. Draw a right triangle having hypotenuse of length 5.4 cm, and one of the acute angles of measure 30 ^{o}**

**Solution 3:**

^{o}.

^{o}

^{o}− 30

^{o}− 90

^{o}= 60

^{o}

**Construction:**

^{o}angle CBY.

^{o}angle BCX on the same side of BC as Y, with X on the same side of BC as Y.

**Question :4. Construct a right triangle ABC in which AB = 5.8 cm, BC = 4.5 cm and ∠C = 90 ^{o}.**

**Solution 4:**

**Construction:**

**Question :5. Construct a right triangle, right angled at C in which AB = 5.2 cm and BC= 4.6 cm.**** **

**Solution 5:**

**Construction:**

^{o}