Using ruler and a pair of compasses only construct a quadrilateral ABCD with |AB|=9cm, |BC|=10cm, |AD|=7.5cm, angle ABC =45°and angle BAD =135°
Using a straightedge and compass only, you cannot mark lengths.
But, since you seem to want them, assume you can in fact mark desired lengths.
Draw a line AB of length 9
At B, construct a circle of radius 10
Construct a right angle at B and bisect it. That will make it 45°. Where the angle intersects circle B will be point C.
At A construct a circle of radius 7.5
At A, construct a right angle. Extend AB past A, and bisect the angle outside AB. That will form an angle of 90+45 = 135°.
Where the angle intersects the circla at A will be point D.
Finally, draw line CD.
I won't the answer
Using a ruler and a pair of compasses only construct a quadrilateral ABCD such that angle BAD =60 degrees angle ABC 135 degrees AB 6.5cm AD 8.5 CD 11cm
To construct a quadrilateral ABCD with the given specifications using only a ruler and a pair of compasses, follow these steps:
1. Take your ruler and draw a straight line segment AB of length 9 cm. This will be one side of the quadrilateral.
2. With A as the center, use the compass to draw an arc with a radius of 10 cm, intersecting the line segment AB. Call the point of intersection C.
3. From point C, use the compass to draw an arc with a radius of 7.5 cm. Let this arc intersect side AB at point D.
4. Draw a line segment CD to complete the quadrilateral.
5. To verify that the angles meet the specifications, use the compass to measure an angle of 45° from segment AB at point B and draw a line. Label the point of intersection with CD as E.
6. Measure an angle of 135° from line segment AB at point A and draw another line. Label the point of intersection with CD as F.
7. The points E and F should coincide with points D and C, respectively, if the angles have been constructed accurately. Label your final points as A, B, C, and D.
8. You have now constructed the quadrilateral ABCD with |AB| = 9 cm, |BC| = 10 cm, |AD| = 7.5 cm, angle ABC = 45°, and angle BAD = 135°.
Remember to be precise with your measurements and construction to ensure accurate results.