Construct triangle ABC such that |AB|=8cm ∆ABC=60° and BAC=45° extend AC to D and EBC to meet at F, construct a perpendicular from F to meet at |BE| at G
To construct triangle ABC with the given specifications and find point G, follow the steps below:
Step 1: Draw a line segment AB of length 8 cm. This will be one side of the triangle ABC.
Step 2: At point A, construct an angle of 45 degrees. To do this, use a protractor, place the center of the protractor at point A, and draw an arc from the baseline to intersect line segment AB. Label the intersection point as C.
Step 3: From point C, draw a line segment extended beyond point A. This will be the line segment AC.
Step 4: Construct a perpendicular bisector of line segment AB. To do this, use a compass, place the needle at point A, extend the compass beyond point B, and draw an arc on both sides of line segment AB.
Step 5: Repeat step 4 for point B. Place the compass needle at point B, extend the compass beyond point A, and draw arcs intersecting the arcs from step 4. Label the intersection point as E.
Step 6: From point C, draw a line segment extended beyond point E. This will be the line segment CE.
Step 7: Draw a line segment from point B to point E. This will be the line segment BE.
Step 8: Extend line segment BE beyond point E. Label the extended line segment as FG.
Step 9: Perpendicular to FG, construct a line segment from point F towards the line segment BE.
Step 10: The point of intersection of the line segment from step 9 and the line segment BE is the point G you are looking for.
You have now constructed triangle ABC with the given specifications and found point G.