Embed Size (px)
DESCRIPTION
Constructing Congruent Angles Step 1: Draw a ray with endpoint S. A Step 2: With compass at point A, draw an arc that intersects the sides of. Label the points of intersection B and C. Step 3: With same compass setting, put the compass on point S. Draw an arc and label its point of intersection with the ray as R.
Citation preview
Lesson 1.7 – Basic ConstructionsLesson 1.7 – Basic Constructions
Constructing Congruent Segments
Given : AB
Construct : CD so that CDAB
Step 1: Draw a ray with endpoint C.
A B
Step 2: Open the compass to the length of .
AB
Step 3: Put the compass point on C. Draw an arc that intersects the ray. Label the point of intersection D.
Constructing Congruent Angles
Given : AConstruct : S so that S A
Step 1: Draw a ray with endpoint S.
A
Step 2: With compass at point A, draw an arc that intersects the sides of . Label the points of intersection B and C.
A
Step 3: With same compass setting, put the compass on point S. Draw an arc and label its point of intersection with the ray as R.
Constructing Congruent Angles
Given : AConstruct : S so that S A
Step 4: Open the compass to length BC. With same compass setting, put the compass point on R. Draw an arc to locate point T.
A
Step 5: Draw ST.
Constructing the Perpendicular Bisector
Perpendicular Bisector: A line, segment, or ray that is perpendicular to the segment at its midpoint, bisecting the segment into two congruent segments.
A B
m
Constructing the Perpendicular Bisector
Step 1: Put the compass point on point A and draw a long arc. Make sure the opening is greater than half of AB.
Step 2: With the same compass setting, put the compass point on point B and draw another long arc. Label the points where the two arcs intersect as X and Y.
Given : AB
Construct : XY so that XY AB
at the midpoint M of AB
A B
Step 3: Draw XY. The point of intersection of AB and XY is M, the midpoint of AB.
Constructing the Angle Bisector
Angle Bisector: A ray that divides an angle into two congruent coplanar angles.
K
J
L
N
Constructing the Angle Bisector
A
Step 2: Put the compass point on point C and draw an arc. With the same compass setting, draw an arc using point B. Label the point where the two arcs intersect as X.
Step 1: Put the compass point on vertex A. Draw an arc that intersects the sides of . Label the points of intersection B and C.
A
Given : AConstruct : AX, the bisector of A
Step 3: Draw AX.
