Question

Construct a quadrilateral ABCD, given that AB = 4 cm, CD = 4.5 cm, AD = 5 cm, ∠A = 70°, and ∠D = 120°.

A) Use a protractor and ruler to construct it.
B) It's impossible to construct based on the given information.
C) Use a compass and straightedge to construct it.
D) Use a calculator to compute the coordinates of the vertices.

Answer 1

To construct quadrilateral ABCD with the given information, use a compass and straightedge.

Step-by-step explanation:

To construct quadrilateral ABCD given the information provided, we can use a compass and straightedge. Step by step:

1. Draw a line segment AB and mark it with a length of 4 cm.
2. Using a protractor, measure ∠A and draw a ray from point A at an angle of 70°.
3. Use a compass to measure a distance of 5 cm from point A along ray AB and mark point D.
4. Measure ∠D using a protractor and draw a ray from point D at an angle of 120°.
5. Set the compass to a length of 4.5 cm and draw an arc from point D intersecting ray AD at point C.
6. Draw the line segment CD connecting points C and D.
7. Finally, draw the line segment BC connecting points B and C to complete the quadrilateral ABCD.