Question 1

-Use the drawing provided to explain the following theorem.
"The three angle bisectors of the angles of a triangle are concurrent."
Given:  ,  , and  are the angle bisectors of the angles of  Prove:  ,  , and  are concurrent at point Z

Accepted Answer

Let point Z name the point of intersection of the angle bisectors  and  . Because  bisects  , every point on  (including Z) is equidistant from the sides of  .
With  and  , it follows that  . With respect to  , also note
that  . Because Z lies on angle bisector  , we also have  . By the Transitive Property of Congruence,  . With point Z being equidistant from the sides of  , Z must also lie on angle bisector  . Thus,  ,  , and  are concurrent at point Z.

Question 2

-Supply missing reasons for the following proof.
Given:  bisects  ;  and  Prove:  S1.  bisects  ; R1.  and  S2.  R2.
S3.  and  are rt.  R3.
S4.  R4.
S5.  R5.
S6.  R6.
S7.  R7.

Accepted Answer

R1. Given
R2. Definition of angle-bisector
R3. Perpendicular lines form right angles.
R4. All right angles are congruent.
R5. Identity
R6. AAS
R7. CPCTC

Question 3

-Supply missing statements and missing reasons for the following proof.
Given: Point X not on  so that  Prove: X lies on the perpendicular-bisector of  S1. R1.
S2.  R2.
S3. With M the midpoint of  , R3.
draw  S4. Then  R4.
S5. Also,  R5.
S6. R6. SSS
S7.  R7.
S8. R8. Definition of perpendicular-bisector of a line segment

Accepted Answer

S1. Point X not on  so that  R1. Given
R2. Definition of congruent line segments
R3. Through 2 points, there is exactly one line.
R4. Definition of midpoint of line segment
R5. Identity
S6.  R7. CPCTC
S8. X lies on the perpendicular-bisector of

Question 4

-Use the drawing provided to explain the following.
Given:  ,  , and  are the medians of  Prove:

Accepted Answer

The answer of 
-Use the drawing provided to explain the...

Exam 7: Locus and Concurrence

-Use the drawing provided to explain the following theorem. "The three angle bisectors of the angles of a triangle are concurrent." Given: , , and are the angle bisectors of the angles of Prove: , , and are concurrent at point Z

-Supply missing reasons for the following proof. Given: bisects ; and Prove: S1. bisects ; R1. and S2. R2. S3. and are rt. R3. S4. R4. S5. R5. S6. R6. S7. R7.

-Use the drawing provided to explain the following. Given: , , and are the medians of Prove: