Using a pair of compasses, a ruler and a pencil. Construct a triangle CDE in which DE =10Cm Dc=8cm and< CDE=45 dregrees. Contract a line, CF, perpendicular to DE such that F lies on DE. Using a protractor, measure and state the size of angle < DCE.
How can I do this
To construct triangle CDE:
1. Begin by using the ruler to draw a line segment, DC, of length 8 cm.
2. On point D, use the compass to mark an arc with a radius of 10 cm.
3. On point C, use the compass to mark an arc with a radius of 8 cm. The arc should intersect the previously marked arc to form point E.
4. Connect points D and E with a straight line segment. This represents the side DE of the triangle.
5. To construct the perpendicular line CF, place the compass at point C and draw an arc that intersects DE.
6. Without changing the compass width, place the compass at point F (where the arc intersects DE) and draw another arc that intersects the previous arc.
7. Finally, draw a straight line segment connecting point C to the intersection of the two arcs (point F).
To measure angle DCE:
1. Take a protractor and align its baseline along the line segment DE.
2. Locate point C on the protractor and read the angle value where it intersects the line segment DC.
3. This measured value represents the size of angle < DCE.
To construct the triangle CDE, follow these steps using a pair of compasses, a ruler, and a pencil:
1. Draw a line segment CD of 8 cm using a ruler.
2. Place the compasses' needle on point C and adjust the distance to 10 cm on the ruler.
3. Without changing the compasses' width, draw an arc that intersects the line segment CD. Label the intersection point as E.
4. With E as the center, adjust the compasses to a shorter length and draw an arc that intersects the previous one. This creates another point of intersection labeled as D.
5. Use a ruler to draw the line segments DE and CE to complete the triangle CDE.
To construct a line CF perpendicular to DE with F lying on DE:
1. Place the compasses' needle on point E and adjust the width slightly longer than half the length of DE.
2. Draw an arc that intersects with DE on both sides, creating two intersection points on DE.
3. Label one of the intersection points as F.
To measure the angle < DCE using a protractor:
1. Place the center of the protractor on point C, aligning one of the protractor's arms with line segment CD.
2. Read the angle measurement on the protractor where line segment CE intersects the scale.
By following these construction and measurement steps, you can now determine and state the size of angle < DCE.