In this lesson, you will use the ASA Postulate to construct a triangle congruent to ABC , (seen in the GeoGebra file below). Directions: Step 1 Begin by constructing a ray in the same direction as BC , placing it towards the bottom of the drawing area. Select the ray icon, and construct ray DE.
Step 2
To duplicate B , you must measure it. Select the angle measuring icon, and click on points C, B, and A (in that order.) Notice that this angle is named .
Step 3
Now select the angle (of given size) icon, and click on points E and D (in that order). You will now get a dialogue box requiring an angle measure. Delete the given number and click on the symbol in the right hand drop-down menu. Select the "counterclockwise" button, then click OK. This should have placed an angle along ray DE with a point F in the general direction of the angle.
Step 4
Select the ray (through two points) icon, and construct ray DF.
Step 5
Right click on the segment between points B and A, noticing that the segment is named "a." Select the circle (center and radius) icon, and click on point D. In the dialogue box, type "a" and click OK.
Step 6
Select the point of intersection icon , and place a point (G) at the intersection of this circle and ray DF.
Step 7
Select the segment icon, and construct DG . You have just constructed a segment congruent to BA . Because you no longer need ray DF or point F, right click on any object bringing up the properties and deselect "Show objects" for both.
Step 8
Next you must construct an angle congruent to A . To do this A must be known so it must be measured. Select the angle measuring icon , then click on points B, A, and C, (in that order.)
Step 9
Select the angle (of given size) icon , and click on points D and G (in that order). You will get a dialogue box requiring an angle measure. Delete the given number and click on the symbol in the right hand drop-down menu. Select the "counterclockwise" button, then click OK. This should have placed an angle along ray DG with a point H in the general direction of the angle.
Step 10
Select the ray (through two points) icon, then click on point G and H. From here, I am confident that you can complete the triangle construction. Once complete, bring up the "properties" menu and deselect "Show objects," hiding all points, rays and any other unnecessary objects. Finally, move the points necessary to place one triangle on top of the other, demonstrating two congruent triangles. CONGRATULATIONS on your successful construction.