Constructing Angles

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In this section you will learn constructing angles.
"Construction" in Geometry means to draw shapes, angles or lines accurately.
In constructing-angles, mostly we use compass and ruler.

Construction of Angles equal to a given angle

Draw an angle of measure 700. Make a copy of it using ruler and compasses.

Step 1: With the help of a protractor, draw an angle ∠DAP of measure 700.

Step 2: Draw a line l and a point P on it.

Step 3: Place the compasses at A and draw an arc to cut the rays of ∠A at B and C.


Step 4: Use the same compasses setting to draw an arc with P as center, cutting l in Q.

Step 5: Set your compasses to the length BC with the same radius.

Step 6: Place the compasses pointer at Q and draw the arc to cut the arc drawn earlier in R.

Step 7: Join PR. This gives ∠P. It has the same as ∠DAP.

∴ ∠DAP = ∠RPQ.

Example 2 : Draw an angle of 600 using compass and then draw a copy of angle 60.
Steps of constructing angles :
Step 1 :Draw a ray PC.
Step 2 : Place the pointer of the compasses at P and draw an arc of convenient radius which cuts the ray PC at a point A.
Step 3 : With the pointer at A (as centre) and with same radius now draw an arc that cuts the previous one at point B.
Step 4 : Join PB. We obtain ∠BPA whose measure is 600.
step 5 : Now draw another ray XY
Step 6 : Place the pointer of the compasses at X and draw an arc of convenient radius which cuts the ray XY at a point M.
Step 7 : With the pointer at M (as centre) and with same radius now draw an arc that cuts the previous one at point N.
Step 8 : Join XN. We obtain ∠NXM whose measure is equal to ∠BPA = 600.

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Practice

1) Given angle is 350. Construct an angle which equal to 350.
2) for obtaining angle 1050, which two angles you will bisect.
Geometrical Constructions

Basic Geometric Constructions
Construction of Line Segment
Bisecting a Line Segment
Constructing Angles
Bisecting Angles
Constructing Parallel Lines
Construction of Triangle (SSS)
SAS Triangle Construction
ASA Triangle Construction
HL Triangle Construction (Rhs -construction)
Constructing Quadrilaterals
Constructing Triangles(when sum of sides or perimeter is given)

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