To construct an angle equal to a given angle

Given:

ABC and line EF

Required: To construct an angle equal to

ABC on the line EF

Procedure:

given angle equivalent angle

With B as a center and with any radius, use the compass tool to construct a circle intersecting AB at G, and BC at H.

Use the segment command under the construct menu and construct segment BH.

Use the circle by center + radius command under the construct menu and construct a circle with E as the center and radius congruent to segment BH.

Label the point of intersection of this circle and the line EF, point K

Use the segment command under the construct menu and construct segment HG.

Use the circle by center + radius command under the construct menu and construct a circle with K as the center and radius congruent to segment HG.

Label the intersection of these two circles as point M.

Use the ray command under the construct menu and construct ray EM.

MEK is the required angle.

Proof:

BH = EK, BG = EM, and HG = KM (radii of = circles are =.)

GBH

MEK (s.s.s.= s.s.s)

ABC=

MEK. (corresponding parts of

Sketch: Use the interactive sketch below and drag point A, B, or C. When does the angle change? Does

MEK change as well?

congruent angle