Warm-Up : EOC Prep . What is RS? What is m<ABC?. Bisectors in Triangles 5.2. Today’s Goals By the end of class today, YOU should be able to…. 1. Define and use the properties of perpendicular bisectors and angle bisectors to solve for unknowns.
What is RS?
What is m<ABC?
Today’s GoalsBy the end of class today, YOU should be able to…
1. Define and use the properties of perpendicular bisectors and angle bisectors to solve for unknowns.
2. Locate places equidistant from two given points on a map.
We learned in chapter 4 that ΔCAD ≅ ΔCBD. Therefore, we can conclude that CA ≅ CB, that CA = CB, or simply that C is equidistant from points A and B.
If CD is the perpendicular bisector of both XY and ST, and CY = 16. Find the length of TY.
We know from the Perpendicular Bisector Theorem that CS is equivalent to CT
CS = CT
CY – CT = TY
Subtract to find the value of TY
If CD is the perpendicular bisector of both XY and ST, and CY = 16. Find the length of CX.
Find the value of x, then find FD and FB:
From the diagram we see that F is on the bisector of ACE. Therefore, FB = FD.
FB = FD
5x = 2x + 24
3x = 24
x = 8
Divide by 3
FB = 5x = 5(8) = 40
FD = 40
Does point A lie on an angle bisector of <TXR? Explain.
Construct an angle ABC
Place the compass point on the angle vertex with the compass set to any convenient width
From where an arc crosses a leg, make an arc in the angle's interior, then without changing the compass width, repeat for the other leg
Draw a straight line from B to point D, where the arcs cross
Done. The line just drawn bisects the angle ABC
A mysterious map has come into your possession. The map shows the Sea Islands off the coast of Georgia. But that’s not all! The map also contains three clues that tell where a treasure is supposedly buried!