Using a ruler and pair of compasses, Construct triangle ABC with AB=10cm, angle ABC=30 and angle BAC=45 .1.a perpendicular from C to AB at D. 2.measure|CD|
To construct triangle ABC with the given measurements and find the length of CD, follow these steps using a ruler and a pair of compasses:
Step 1: Draw AB
Using the ruler, draw a line segment AB of length 10 cm. Let A be the starting point and B be the endpoint.
Step 2: Construct angle BAC
At point A, draw an angle of 45 degrees using the compass. Place the compass point on point A and open it wide enough to intersect line AB on both sides.
Step 3: Construct angle ABC
At point B, draw an angle of 30 degrees using the compass. Place the compass point on point B and open it wide enough to intersect line AB. Label the point of intersection as C.
Step 4: Construct a perpendicular from C to AB at D
Using the compass, set the width to more than half of line segment AB. Place the compass point on point C and draw arcs anywhere above and below line AB.
Without changing the compass width, place the compass point on the intersections of the arcs and draw two arcs intersecting each other. Label the point of intersection as D.
Step 5: Measure CD
Using the ruler, measure the length of line segment CD starting from point C to point D. The measurement will give you the length of CD.
Once you have completed these steps, you will have successfully constructed triangle ABC and measured the length of CD.