RT = 16
AB = 5
HJ = 6
Step-by-step explanation:
To start off a perpendicular bisector is a bisector that makes a 90° angle, and a bisector divides something into two equal parts.
1. So for the first triangle it is asking for the line RT, and the bisector (RT) goes between the angle < TRS. With this being said, the lines RT is equal to the line RS, so since RS is 16 so is RT. So the answer is RT= 16.
2. So for the second triangle it is asking for the line AB, and line AB is bisected by line t the lines AD and DB are equal. So knowing this they both are 2.5, but the question isn't asking for part of the line, it is asking for the whole thing so you have to add 2.5 + 2.5. After you adding you get solution of 5 which makes AB = 5.
3. So for the third triangle its is asking for the line HJ, and the bisector (HL) goes between the angle < JHK. With this being said the lines HJ and HK are equal to one another. So you would write that as an equation which is 3x + 1 = 5x - 3. So for this part can vary, you can either move the x to the left or the right either way it gets you the answer, but I am going to explain how to move it to the left. First, you want to subtract 5x to 3x because when you move a variable to the other side of the equation (=) you have to do the opposite value so the number on the other side can cancel out. So on the right the 5x cancels out as it is subtracted by the 3x. Then, you do the same thing but with the 1. You will subtract 1 from -3 because you have to have something on both sides of the equation. After you did these two steps the equation is now -2x = -4. The main reason for doing this equation is to get the x alone so to do that you have to divide -4/-2. The reason why you don't change the sign is because like I said you are trying to cancel out the number you are moving so a negative divided by a negative equals a positive so you would just divide the -2. After this last step you get x = 2. But the problem is asking for the line not what x is. So you put your x into the equation since you have the number that is missing. So your new equation should look like 3 × 2 + 1. Then the answer you get from this should be 6, so which makes HJ = 6.
