8. Similar parts
Choice a
9. The Law of Sines says a:b:c and 
are the same ratio.
The sines will go in order for acute angles, we have to convert 120 to its supplement 60 and then the order is 29,31,"60" or opposite sides JK, KL, JL
choice b
10.
DEF and FEG are supplments, FEG=180-DEF=180-114=66
DEF and HEG are opposite angles, so congruent HEG=DEF=114
chioce a
Answer:
Read the problem carefully. For the purposes of this step-by-step geometry proof, use the following example: Given that triangle ABC is an equilateral triangle and that line AD bisects line BC, prove that the resulting triangle ABD is a right triangle.Draw an illustration of the problem. Having a picture in front of you when doing a geometry proof really helps organize your thoughts.Consider what you know about each piece of given information. For example, because ABC is an equilateral triangle, all three sides must be the same length. Furthermore, all three angles must be equal as well. Since a triangle contains 180 degrees, then each angle in an equilateral triangle must measure 60 degrees. Moving on to the other piece of given information, since line AD bisects side BC, that makes line segments CD and DB equal in length.Use the facts established by the given information to generate more facts that are useful to your geometric proof. Since the line segments CD and DB are equal in length, that means the angle CAD must be equal to the angle DAB.Extrapolate from the facts to get closer to the solution. Since angle A is 60 degrees, the smaller angles must be one half of 60, or 30 degrees. Given that angle B is 60 degrees and that angle DAB is 30 degrees, this accounts for 90 degrees of a triangle. The remaining 90 degrees must be contained in the angle BDA. Since a right triangle must contain a 90-degree angle, you have just proven that triangle ABD is a right triangle.Write out the step-by-step geometric proof of the problem in a two-column format. In the left hand column, write a statement and in the right hand column, write the proof of the statement. Repeat this process until you have documented all of the steps in your thinking process that resulted in your solution.
Step-by-step explanation:
<h3>
Step-by-step explanation:</h3>
The point of intersection of the perpendicular bisectors of a triangle is the circumcenter, the center of the circle that contains the three triangle vertices.
If that center is on one side, that side must be a diameter of the circle. The diameter cuts the circle into two arcs, each of which measures 180°.
The third vertex of the triangle and its two legs form an inscribed angle that subtends an arc of 180°. The measure of that angle is half the measure of the arc, so the angle measures 90° and is a <em>right angle</em>.
A triangle with a right angle is a right triangle. QED
