Please answer 6 thru 8 in detail will reward with points tha

GEOMETRY -Alternate Exam 5- Continued Student Number Student\'s Name 6. Given: AABC with midpoints M. P and N as shown Finish the following: Then MP, MN, and NP are of A ABC. AM MB IIAC, MN 7. Circle the comect swer below for the diagram to the right. If is the perpendicular bisector of AB, then AD BD AC BC All of these E is on CD 8. CD is the perpendicular bisector of AB. Find the length AB,AD, and AE. AB Is point Eon CD? (Answer yes or no and explain.) AMERICAN SCHOOLLansing, IL A(2509-0AN12-05 x+y-1

Solution

6. (i) Midsegments of the triangle

(ii) MP parallel to AC

(iii) The line joining the midpoints of two sides of a triangle is parallel to third side and half of it.

Hence MN = 1/2 BC

(iv) The four small triangle are congruent hence

AM = MB = AN = NC = BP = PC

(7) In ACD and BCD

AC = BC (since CD bisect it into two equal parts)

CD = CD (common side)

and <ACD = <BCD = 90^o

Hence by SAS ACD is congruent to BCD

AD = BD

then all of the above are true options.

(8) CD is the perpendicular bisector of AB so AD = DB

2x = 5x-9 => 3x =9 => x =3

Hence AB = 7x - 9 = 21 - 9 =12

AD = BD = 3x-1 =8 (Since ACD and BCD are congruent By CPCT AD = BD)

AE = x + y -1 = x + 3x-1 -1 = 4x - 2 = 10

by the Converse of the Perpendicular Bisector Theorem, if E was on the perpendicular bisector of CD, then segments AE and segments BE would be congruent. Hence E is not on line CD