Construct a triangle ABC in which AB=AC=5.2cm and angle A= 120 degree. Draw Ad perpendicular to BC. Use ruler and compass.
What do you mean by 'you can do that'. If I could do it then why would I come here to get the answer.
Why did the triangle go to the bakery?
Because it wanted to get a good loaf of bread-crumbs for its path!
Now, let's get started with drawing triangle ABC. Follow the steps below:
Step 1: Draw a line segment AB of length 5.2 cm using a ruler.
Step 2: Place the compass at point A and draw an arc with radius 5.2 cm. This arc should intersect AB at two points. Mark these points as C and C'.
Step 3: Draw a line segment BC' of length 5.2 cm from point B.
Step 4: Bisect the line segment BC' and draw a perpendicular line through the midpoint of BC'. This perpendicular line will meet AB at point D.
Step 5: Connect points A and C, A and D, and C and D to form triangle ABC.
And ta-da! You have successfully constructed triangle ABC where AB = AC = 5.2 cm and angle A = 120 degrees, with Ad perpendicular to BC.
To construct a triangle ABC with the given conditions using only a ruler and compass, follow these steps:
1. Draw a line segment AB of length 5.2 cm using a ruler.
2. Place the compass on point A and adjust its width so that it reaches point B. Without changing the width, draw an arc that intersects the line segment AB at two points, let's name them C1 and C2.
3. Draw two arcs from C1 and C2 with the same compass width and set the radius to a length greater than half of AB. These arcs should intersect each other above AB. Label the point of intersection as P.
4. Now, take P as the center and draw an arc with a radius greater than the distance between P and A. This arc should intersect the extension of AB at point Q.
5. Draw the line segment AQ using a ruler.
6. Construct the angle of 120 degrees at point A. To do this, place the compass tip on point A and draw an arc that intersects the line segment AQ on both sides. Label the points of intersection as X1 and X2.
7. With compass width unchanged, place the tip on point X1 and draw an arc that intersects the previously drawn arc at point Y1. Similarly, draw an arc from X2 to intersect the previously drawn arc at point Y2.
8. Now, draw a line segment from A to the point of intersection between the arcs Y1 and Y2.
9. Extend the line segment AQ beyond point A.
10. Set the compass width to the distance between points A and Q. Place the compass tip at point Q and draw an arc that intersects the extended line segment AQ.
11. With the compass width unchanged, place the tip on the intersection of the arc and extended line segment AQ and draw an arc that intersects the previously drawn segment AB. Label this point of intersection as C.
12. Draw the line segments AC and BC using a ruler.
13. Finally, draw a line segment perpendicular to BC from point A and label the point of intersection with BC as D.
Now you have successfully constructed triangle ABC, where AB = AC = 5.2 cm, and angle A = 120 degrees. The line segment AD is perpendicular to BC.
Kumari
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if you can construct a 60° angle, you can do one of 120°.
One of the earliest constructions is a perpendicular bisector, so I'm sure you can do that.
So, draw your 120° angle, label it A, and you have the angle bisector already done.
Mark off AB and AC and connect B and C to form BC.
Your angle bisector is also the perp. bisector of BC.