There are many possible ways to construct a pair of adjacent congruent angles, I’m going to show one way.
First we need to make sure you understand the vocabulary:
Adjacent: To be adjacent to something, means to be right next to each other. So in geometry, the angles that touch each other can be adjacent to each other.
Congruent: To be equal to in length and/or angle degrees.
Radius: Half of a diameter of a circle. Or half the length of a circle.
Vertex: The end point of an angle.
Angle Bisector: A line that makes a big angle into two smaller congruent parts.
The plan is to do an angle bisector.
THE ANGLE BISECTOR METHOD
To start, just draw an angle of any size and degrees you want using a straightedge or a ruler.
You can label your angles if you want, so I’m going to make the vertex B.
After that, take out your compass and draw any sized circle around the vertex of the angle.
Again if you want, you can label the points where the circle intersected A and C.
Next, take your compass and for each point A and C, draw a circle with a radius of AC.
Now this is the cool part, if you noticed, the newly intersected points created by the two circles should line up with B. So using a ruler connect the dots!
Congrats you just made an angle bisector and made adjacent congruent angles!
For more info on how to do this check the following links:These are really helpful, probably more than this explanation!
This is an interactive adjacent angles diagram.http://www.mathopenref.com/anglesadjacent.html
This is for the construction:http://www.mathopenref.com/constbisectangle.html
This is an interactive diagram on :http://www.mathopenref.com/bisectorangle.html
Hope that helped, if you’re still confused you can respond here and maybe I can try to help further.
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