Construct ABCD with AB =5.5cm BC=3.5cm, CD=4cm, AD=5cm, and angle A=45°, with construction steps

9514 1404 393

  see the attachment

Step-by-step explanation:

1. Lay out points A and B so they are 5.5 cm apart.

2. Set the compass to 5 cm and draw arcs that intersect above and below segment AB. Label the intersection points Y and Z.

3. Draw segment YZ as a perpendicular bisector of AB.

4. Label the intersection of YZ and AB point E.

5. Using E as the center and AE as the radius, draw an arc that intersects segment YZ at F.

6. Draw segment AD through F. D will lie on the circle of radius 5 cm centered at A. This segment makes 45° angle DAB.

7. Draw an arc of radius 4 cm centered at D through the vicinity of point C.

8. Draw an arc of radius 3.5 cm centered at B through the vicinity of C. The intersection point with the arc of step 7 is point C.

9. Draw quadrilateral ABCD meeting the given requirements.

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About the attachment

My geometry tool draws circles of a given radius more easily than arcs of a given radius, so you see circles where only arcs are needed.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

step-by-step explanation: