Constructing Angles

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 70 ⁰ . Make a copy of it using ruler and compasses.

Step 1: With the help of a protractor, draw an angle ∠DAP of measure 70 ⁰ .

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.

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Example 2 : Draw an angle of 60 ⁰ 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 60 ⁰ .
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 = 60 ⁰ .

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Practice
1) Given angle is 35 ⁰ . Construct an angle which equal to 35 ⁰ .
2) for obtaining angle 105 ⁰ , which two angles you will bisect.

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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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