Using a ruler and a pair of compasses only. Construct triangle ABC in which angle A=45°, AB=7cm, AC=9cm
ok, I did that, now what?
Answer
To construct triangle ABC with angle A=45°, AB=7cm, and AC=9cm, we will need to use a ruler and a pair of compasses. Follow these step-by-step instructions:
1. Draw a line segment AB using the ruler. It should be 7cm in length. Label the endpoints A and B.
2. Place the compass at point A and draw an arc where the center of the compass is at point B. This arc should intersect the line segment AB. Label this intersection point as C.
3. Now, you have points A, B, and C located. Next, we need to construct the angle A=45°.
4. Place the compass at point A and draw an arc within the angle created between points A and B. Let this arc intersect the line segment AB. Label this intersection point as D.
5. Without changing the compass width, place the compass at point D and draw an arc that intersects the previously drawn arc within the angle.
6. Draw a line segment from point A to the point where the last arc intersects the previously drawn arc. This point of intersection is labeled as E.
7. Finally, draw a line segment from point E to point C.
8. Triangle ABC is now constructed. The angle A should measure 45°, and the line segments AB and AC should measure 7cm and 9cm, respectively.
Remember to double-check your measurements and constructions to ensure accuracy.