Deck 7: Locus and Concurrence

Question 1

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.

Answer 1

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 2

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

Answer 2

If , , and are the medians of , then their point of concurrence is
Q, the centroid of . It follows that . By the Segment-Addition
Postulate, we have . By substitution, . By subtraction, . In turn, or 2. Multiplying the equation by , we have .

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

Answer 3

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 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