Exercise 14.1Exercise 14.2Exercise 14.3Exercise 14.4Exercise 14.5Exercise 14.6 |

**NCERT Answers for Class 6 Maths**

Chapter 14 Practical Geometry Exercise 14.5

Chapter 14 Practical Geometry Exercise 14.5

**Page 286**

**Ex 14.5 Class 6 Maths Question 1. ****Draw \(\overline {\bf AB }\) of length 7.3 cm and find its axis of symmetry.**

**Answer**

**Step 1:** Draw **\(\overline {\bf AB }\)** = 7.3 cm

**Step 2:** Taking A and B as centre and radius more than half of **\(\overline {\bf AB }\)**, draw two arcs which intersect each other at C and D.

**Step 3:** Join C and D to intersect **\(\overline {\bf AB }\) **at E. Thus, CD is the perpendicular bisector or axis of symmetry of **\(\overline {\bf AB }\)**.

**Ex 14.5 Class 6 Maths Question 2. Draw a line segment of length 9.5 cm and construct its perpendicular bisector.
**

**Answer**

**Step 1:** Draw a line segment **\(\overline {\bf AB }\)** =9.5 cm

**Step 2:** With centres A and B and radius more than half of AB, draw two arcs which meet each other at C and D.

**Step 3:** Join C and D to meet **\(\overline {\bf AB }\)**.

Thus, CD is the perpendicular bisector of AB.

**Ex 14.5 Class 6 Maths Question 3. Draw the perpendicular bisector of \(\overline {\bf XY }\) whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY.
**

**Answer**

**Step 1:** Draw a line segment **\(\overline {\bf XY}\) ** = 10.3 cm.

**Step 2:** With centre X and Y and radius more than half of XY, draw two arcs which meet each other at C and D.

**
Step 3:** Join C and D which meets

**\(\overline {\bf XY}\)**.

**Step 4:** Take a point A on **\(\overline {\bf CD}\)**.

(a) On measuring, AX = AY = 5.6 cm.

(b) On measuring, **\(\overline {\bf MX}\) ** = **\(\overline {\bf MY}\)** = 12 XY = 5.15 cm.

**Ex 14.5 Class 6 Maths Question 4. Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.**

**Answer**

**Step 1:** Draw a line segment **\(\overline {\bf AB}\) **= 12.8 cm

**Step 2:** With centre A and B and radius more than half of AB, draw two arcs which meet each other at D and E.

**Step 3:** Join D and E which meets **\(\overline {\bf AB}\)** at C which is the midpoint of **\(\overline {\bf AB}\)**.

**Step 4:** With centre A and C and radius more than half of AC, draw two arcs which meet each other at F and G.

**Step 5:** Join F and G which meets **\(\overline {\bf AC}\)** at H which is the midpoint of **\(\overline {\bf AC}\)** .

**Step 6:** With centre C and B and radius more than half of CB, draw two arcs which meet each other at J and K.

**Step 7:** Join J and K which meets **\(\overline {\bf CB}\)** at L which is the midpoint of **\(\overline {\bf CB }\)** .

Thus, on measuring, we find **\(\overline {\bf AH}\)** = **\(\overline {\bf HC}\)** = **\(\overline {\bf CL}\)** = **\(\overline {\bf LB }\)** = 3.2 cm.

**Ex 14.5 Class 6 Maths Question 5. With \(\overline {\bf PQ }\) of length 6.1 cm as diameter, draw a circle.**

**Answer**

**Step1:** Draw **\(\overline {\bf PQ}\)** = 6.1 cm

**
Step 2:** Draw a perpendicular bisector of

**\(\overline {\bf PQ}\)**which meets

**\(\overline {\bf PQ}\)**at R i.e. R is the midpoint of

**\(\overline {\bf PQ}\)**.

**Step 3:** With centre R and radius equal to **\(\overline {\bf RP}\)** , draw a circle passing through P and Q.

Thus, the circle with diameter **\(\overline {\bf PQ}\)** = 6.1 cm is the required circle.

**Ex 14.5 Class 6 Maths Question 6. Draw a circle with centre C and radius 3.4 cm. Draw any chord \(\overline {\bf AB }\). Construct the perpendicular bisector of \(\overline {\bf AB }\) and examine if it passes through C.**

**Answer**

Step I: Draw a circle with centre C and radius 3.4 cm.

Step II: Draw any chord **\(\overline {\bf AB}\)**.

Step III : Draw the perpendicular bisector of **\(\overline {\bf AB}\)** which passes through the centre C.

**Ex 14.5 Class 6 Maths Question 7. Repeat Question 6, if \(\overline {\bf AB }\) happens to be a diameter.**

**Answer**

**Step 1:** Draw a circle with centre C and radius 3.4 cm.

**Step 2:** Draw a diameter AB of the circle.

**Step 3:** Draw a perpendicular bisector of AB which passes through the centre C and on measuring, we find that C is the midpoint of **\(\overline {\bf AB}\)** .

**Ex 14.5 Class 6 Maths Question 8. Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?**

**Answer**

Step 1: Draw a circle with centre 0 and radius 4 cm.

Step 2: Draw any two chords **\(\overline {\bf AB}\)** and **\(\overline {\bf CD}\)** of the circle.

Step 3 : Draw the perpendicular bisectors of **\(\overline {\bf AB}\)** and **\(\overline {\bf CD}\)**** **i.e. P and S.

Step 4 : On producing the two perpendicular bisectors meet each other at the centre O of the circle.

**Ex 14.5 Class 6 Maths Question 9. Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of \(\overline {\bf OA }\) and \(\overline {\bf OB }\). Let them meet at P. Is PA = PB ?**

**Answer**

**Step 1:** Draw an angle XOY with O as its vertex.

**Step 2:** Take any point A on OY and B on OX, such that OA + OB.

**Step 3:** Draw the perpendicular bisectors of OA and OB which meet each other at a point P.

**Step 4:** Measure the lengths of **\(\overline {\bf PA}\)** and **\(\overline {\bf PB}\)**. Yes, **\(\overline {\bf PA}\)**= **\(\overline {\bf PB}\)**.

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