17.4 Similar and Congruent Figures

CONGRUENT SHAPES

• Same angles
• Same side lengths
• Can be rotated or a mirror image
• A cut-out of one shape will always fit exactly over the othe

SIMILAR SHAPES

• Same angles
• Sides in the same proportion
• Can be rotated or reflected
• One is an enlargement of the other

17.2 Bisect Line Segments and Angles (p. 380-382)

Drawing perpendicular bisector for a line:
Place the sharp end of a pair of compasses at one end of the line, and open it to just over half of the line. Draw an arc which must intersect the line in the position described. Then put the sharp end at the other of the line and, keeping the compassing at the same length, draw another arc which intersects the first one twice and also the line. Then draw a straight line through the two places where the arcs intersect. This line is the perpendicular bisector.

Drawing perpendicular bisector of angle:
Places the sharp end of the compass at the point of the angle and, after having opened it arbitraily wide, draw an arc which intersects the two lines meeting to form the angle each once in the said position. Then remove the compass and, always keeping it opened at the SAME length, place the sharp end at each of the two places where the previous arc cuts each of the two lines meeting to form the angle. In this position with the described length, draw a small arc at each of the said places, which should cross each other. Draw a straight line from the point of the angle to this crossing. This should be the bisector of the angle.

17.1 Congruent Segments and Angles (p.376-379)

I. Congruent: Exactly the same is size and shape

A. Segments: Make congruent line segments by using a compass to measure the length of the original line segment and then marking the same distance with your compass on a ray.

Check out this video from hstutorials.net

Here is another technique from mathopenref.com

B. Angles: Build a congruent angles using a straight edge and compass

1. Draw a ray

2. Draw an arc through the original angle

3. Draw the SAME arc through the ray - label the point of intersection

4. Use a compass to measure the distance between the rays in the original angle

5. Using the same compass opening, mark the distance on the arc through the ray

6. Draw a ray from the endpoint in the original ray through the x formed by the arcs in steps 2 and 5

Check out this video form hstutorials.net