PRACTICAL GEOMETRY chapter 14

Explanation:

Use a ruler to draw a line segment of 7.3cm as follows:

Step 1: Mark point A on the paper

Step 2: Place point 0 on the ruler at A

Step 3: At 7.3cm on the ruler mark point B

Step 4: Now connect A and B

Explanation:

Step 1:Draw a line l and mark a point A on this line

                                  
                                           


Step 2: Place the compass on the ruler 0. Now extend the caliper, place pencil at 5.6cm and make   a mark.
Step 3: Place the compass needle at point A, draw an arc and cut it at point B. The length segment is 5.6cm.

Explanation:

Step 1: draw a line l and mark a point A on it.
Step 2: Set the caliper to 7.8cm, place the compass needle at point A, draw an arc and cut it at B

Step 3: Set the ruler to 4.7cm, make an arc and cut it at C. The pointer placed at point A is a       4.7cm line segment


Step 4:Now place the ruler so that the point 0 of the ruler coincides with point C.
Now read the position of the point B.It will be 3.1cm.

Explanation:

(1) Draw a line l and mark a point P on it.Let AB be the given line segment of 3.9cm


(2) Set the compass to the length of AB, place the compass needle at point p, draw an arc and a straight line to intersect at X.

(3) Then place the cursor at point X,draw an arc and intersect line at point. 

PQ is the required line segment. Using the ruler,we can measure the length 7.8cm.

Explanation:

(1) Given = 7.3 cm and = 3.4 cm


(2) Set the compass to the length of CD, place the compass needle at point A and draw an arc around the point of intersection P of AB.

(3) Adjust the bracket to the length of BP.
Contstruct a line l and mark a point on it.

(4) place the compass pointer at point X and draw an arc and a straight line intersecting at Y is the desired line segment.Now, the difference in the length of the sum

 = 7.3 – 3.4 = 3.9 cm
Use a ruler to measure the length of 3.9 cm.

Explanation:

(1) Let the given line segment be

(2) Set the compass to the length of 
(3) draw any straight line point A on it

(4) Place the cursor on point A, Without changing the compass setting, draw an arc intersecting the line segment at point B is the desired line segment

Explanation:

Build a line segment according to the following steps, so that the length is twice of

(1)Let the given line be

(2) Set the compass to the length of
(3) Draw a line l and mark a point  P on it

(4)Place the cursor on P, draw an arc to intersect the point X of the line segment, without changing the setting of the compass

(5) Place the cursor at point X again with the same radius as before, and draw an arc,the arc intersects the line l at point Q is the required line segment.

Explanation:

(1) Draw a line segment and mark a point M on it.

(2) Take M as the center of the circle, take a suitable radius as the arc and cut the segment from right to points C and D respectively.
(3) With C and D as centers and with radius greater than CM, draw two arcs that intersect at point E.


(4) Join EM. Now perpendicular to
is

Explanation:

Make a structure 7.3 cm long using the following steps and find its axis of symmetry
(1) Draw a line segment 7.3 cm
(2) Take A as the center and draw a circle with a caliper. The radius of the circle must be greater than half the length.


(3) Now take B as the center of the circle and use a compass to draw another circle with the same radius as before.
Let it cut the previous circle at points C and D


(4) Join CD. The axis of symmetry is now

Explanation:

Use the following steps to construct a line segment of length 9.
5 cm and make its center line
(1) Draw a line segment of 9.5 cm


(2) With point P as the center, draw a circle with a compass. The radius of the circle must be greater than half the length of


(3) With point Q as the center, use a compass to draw another circle with the same radius as the original one. Let it cut the previous circle in R and S respectively.
(4) Join RS.
Now the axis of symmetry, which is the center line of the line

Explanation:

(a) Take any point P on the drawn centerline.
Find out if PX = PY.
(b) If M is the midpoint of , what can you say about the lengths MX and XY?
Solution:
(1) Draw a 10.3 cm line segment



(2) use point X as the center of the circle to draw a circle with a compass. The radius of the circle

 must be greater than half the length of
(3) Now take Y as the center of the circle and use a compass to draw another circle with the same radius as before.
Coupons
(4) connecting AB to points A and B of the previous circle. The axis of symmetry here is



(a) Take any point P. We can observe that the length measures of PX and PY are the same
as the axis of symmetry, and any point on it is the same distance from both ends of


(b) M is the center of . The vertical axis will pass through point M. So the length of is twice as long as 2MX = XY.

Explanation:

Construct an angle 600 as follows
(i) Draw a line l and mark a point P on it. With P as the center, make an arc of a circle with a suitable radius and intersect the line l at Q
(ii) With Q as the center and the same radius as before, draw an arc that intersects the arc previously drawn at point R.
(iii) Access to public relations.

PR is the radius needed to cut 600 with line l.

Explanation:

Follow the steps below to make a 300 angle
(i) Draw a line l and mark a point P on it. With P as the center, make an arc of circle with a suitable radius and intersect the line l in Q.
(ii) With Q as the center and the same radius as above, draw an arc at point R to connect with the previously drawn arc.
(iii) With Q and R as centers, draw an arc with radius greater than 1/2 RQ so that they intersect at S. Connect PS with the line l, this is the radius required to make 300 possible.

Explanation:

To construct a measured angle 900
follow these steps

(i) Draw a line l and mark a point P on it. With P as the center, make an arc of a circle with a suitable radius and intersect the line l in Q.
(ii) With Q as the center and the same radius, draw an arc and cut the previously drawn arc at R
(iii) With R as the center and the same radius, draw an arc and cut the arc at S as shown in Figure
(iv) With R and S as centers, draw an arc of the same radius that intersects at T.
(v) Connect PT, which is the radius needed to intersect line l at 900.

Explanation:

To construct a measured angle 1200
do the following (i) Draw a line l and mark a point P on it. With P as the center, make an arc of a circle with a suitable radius, so that it intersects the line l in Q.
(ii) With Q as center, draw an arc of the same radius and intersect the arc drawn before in R.
(iii) With R as center, draw an arc of the same radius so that it intersects the arc in S as shown in the figure.
(iv) Add PS, the radius 16 needed to form 1200 with the line l

Explanation:

To construct the measured angle 450
as follows: (i) Draw a line l and mark on it a point P. With P as center, make an arc of a circle with a suitable radius and cut the line l in Q.

(ii) Take Q as center, draw an arc of the same radius and cut the arc drawn before in R

(iii) Take R as the center, draw an arc of the same radius and make the arc intersect in S, as shown in the figure Show.
(iv) Take R and S as centers and draw arcs of the same radius so that they intersect at T.
(v) Join PT.
Let it intersect the main arc at point U.
(vi) Now take Q and U as centers and draw an arc of radius greater than 1/2 QU which intersects at point V. Connect the PV.
PV is the desired radius at 450 from the line l

Explanation:

 Follow the steps below to construct the measured angle 1350
(i) Draw a line l and mark a point P.
Taking P as the center and taking a suitable radius, draw a semicircle in Q and R to cut with the line l.
(ii) Take R as center, draw arc with same radius and cut previous arc at S
(iii) Take S as center, draw arc with same radius and cut arc with S at T as shown in Figure
( iv) With S and T as centers, draw an arc with the same radius and cut it in U.
(v) Join PU. Let it intersect the arc in V. Now take Q, V as the center of the circle and the radius is greater than 1/2QV, draw an arc intersecting in W.
(vi) Connect PW to line l

1350

Explanation:

Follow the steps below to create Measure Angle 700 and a copy of it.
(i) Draw a line l and mark a point O on it.
Now center the protractor at point O and the zero edge along line l.
(ii) Mark point A at measured angle 700. Join the OA. Now OA is the radius forming 700 from the right l. With point O as the center, draw an arc with an appropriate radius at an angle of 700 degrees.
Let it cut two radii at the 70° angle at points B and C respectively
(iii) Draw a line m and mark a point P on it. Draw the arc again with the same radius as before, centered in P. Let him cut the line m at point D
(iv) Adjust the compass to the length of BC. Use this radius to draw an arc centered at D that intersects the arc drawn earlier at point E.
(v) Connect PE.
Here PE is the desired radius at the same angle of measure 700 as the line m

Explanation:

Construct a copy of the measured angle 450 and its supplementary angle
as follows (i) Draw a line segment and mark a point O on it. Center the protractor at point O and along the zero edge of the straight segment.
(ii) Mark a point A where the angle 400 is measured. Join the OA. Here OA is the desired radius to make 400. ∠POA is the extra angle of 400
(iii) With point O as the center, draw an arc with appropriate radius inside ∠POA. Let it intersect with the two radii of ∠POA at points B and C respectively.
(iv) Draw a straight line m and mark a point S on it. Again draw an arc centered in S and with the same radius as before. Let it cut line m at point T.
(v) The compasses are now adjusted to the length of BC. With T as the center, draw an arc with this radius, intersecting the previously drawn arc at point R.
(vi) Join RS. Here RS is the desired radius at the same angle with the line m in complement of 400 [ie 1400]

Explanation:

Construct an angle of 750° and its axis of symmetry as follows:
(i) Draw a line l and mark two points O and Q on it.
Draw an arc at a suitable radius with the center O. Let this line l intersect at R
(ii) centered at R, and with the same radius as before, draw an arc so that it intersects the arc previously drawn at S
(iii) same radius as before, Take S as center, draw arc and cut arc at point T. As shown in Figure
(iv) Take S and T as center, draw arc of same radius and make them U-intersect.
(v) Add OR . Let it cut the arc into V. Now take S and V as midpoints to draw an arc with radius greater than 1/2 SV. Let them cross at P.
Join the OP. Now OP is the radius forming 750 from the right l.
(vi) Let this ray intersect our main arc at point W. With R and W as the center, draw an arc with a radius greater than 1/2 RW inside the interior angle 750 and intersect it at point X.
Reliant OX
OX is the axis of symmetry of ∠POQ = 750

Explanation:

Construct a measured angle 1470 and its axis
as follows: (i) Draw a line l and mark the point O on it. Center the protractor at point O and along the zero edge
of line l (ii) mark point A at measured angle 1470. Connect the OAs.
Now OA is the radius
needed to make 1470 with line l (iii) With point O as center, draw an arc with appropriate radius. Let it cut two radii at an angle of 1470 at points A and B.
(iv) With A and B as centers, draw an arc of radius greater than 1/2AB in the internal angle 1470, cut at point C and join OC.

OC is the required bisector of the angle 1470

Explanation:

Follow the steps below to construct a right angle and its bisector.
(i) Draw a line l and mark a point P on it. Take point P as the center to create an arc of a circle with an appropriate radius.
Let this line intersect l at R
(ii) take R as the center and draw an arc with the same radius as before, and have it intersect with the previously drawn arc at S
(iii) take S as the center and the same radius as before, draw a circle The arc intersects the arc at T as shown in Figure
(iv) Take S and T as the center, draw an arc with the same radius and cut at U.
(v) Join PU. PU is the desired radius perpendicular to line l. Let this main arc intersect at point V.
(vi) Now centered on R and V, an arc of radius greater than 1/2 RV is drawn intersecting at point W.
Join the private server.

PW is the centerline required for this right angle.

Explanation:

Construct a measured angle 1530 and its axis
as follows:

(i) Draw a line l and mark a point O on it.Center the protractor at point O and along the zero edge of line l

(ii) mark point A at the measure of angle 1530. Join the OA. Now OA is the desired radius to make 1530 and line l

(iii) Draw an arc of circle of appropriate radius centered at point O. Let it intersect two rays at angle 1530 at points A and B.

(iv ) With A and B as centers, draw an arc with radius greater than 1/2AB inside angle 1530.

Let them intersect at C. Add OC
(v) So that OC intersects the main arc at point D. From centers A and D and centers D and B draw an arc of radius greater than 1/2 AD . Let them intersect at points E and F respectively. Now add OE and OR
OR, OC, OE are the radii that divide the angle of 1530 degrees into four equal parts.

Explanation:

The required circle can be drawn as follows:
The first step: For the required radius of 3.2 cm, first open the compass.
Step 2: For the center of the circle, mark point "O".
Step 3: Place the compass cursor on the "O".
Step 4: Now slowly turn the compass to draw the desired circle.

Explanation:

The desired circle can be drawn like this:
Step 1: For the desired radius of 4 cm, first open the compass
Step 2: For the center of the circle, mark a point 'O'
Step 3 : Place the compass needle on the "O" .
Step 4: Slowly rotate the compass to draw a circle.
Step Five: Then open the compass 2.5 cm.
Step 6: Move the compass pointer to "O" again and slowly rotate the compass to draw a circle

Explanation:

We can draw a circle with center "O", or any convenient radius. Let AB and CD be the two diameters of the circle.
When we connect the points of these diameters, a quadrilateral is formed.


We know that the diameters of the circles are of the same length, so the diagonals of the quadrilaterals formed are also of the same length. Chapter
It will be a rectangle. Chapter

We can now see that the connection of the points of these diameters together forms a quadrilateral.


We can find that OD = OE = OR = OG = radius r.
In this quadrilateral DFEG, the diagonals are equal and perpendicular to each other. They also bisect each other, so it will be a square.
To check our answer, we can measure the lengths of the sides of the quadrilaterals formed.

Explanation:

We can draw a circle and the required three points A, B, C as follows:

Explanation:

Let's draw two circles with the same radius passing through the center of the other circle.


Here points A and B are the centers of these circles which intersect respectively at points C and D.
Now in the quadrilateral ADBC  we can observe:
AD = AC [radius of the circle centered in A]
BC = BD [radius of the circle centered in B]
because the two circles have equal radii.
Therefore AD = AC = BC = BD
The quadrilateral ADBC  is therefore a rhombus and bisects at 900 with the lines of the rhombus. So and are rectangles.