Question

can you guys please please help me with question 14 in the photo.. please help me

Answer 1

Hey!! here's your Answer-

1.. In triangles ABX and QCX
AB is parallel to CQ (AB is Parallel to CD and CD is Produced to Q)
therefore, angle BAX = XQC --Alternate angles
and. angle ABX = XBQ---Alternate angles
also. BX = XC --- X is M.P
therefore trBAX is congruent to tr XQC by AAS congruence criterion.

2.. From above AB = CQ -- CPCT
Given,. AB = DC and AB = QP
therefore AB = DC =QP.

Answer 2

Solution:-

☆ In Triangle ABX & QCX

/_ AXB = /_CXQ (Vertically Opposite Angle)

/_XAB = /_ XQC (Alternate Interior angle)

=> Triangle ABX & QCX are Congruent by AA.

=> By CPCT,

AB = CQ. ___________(1)

☆ Given AB = CD,_________(2)

From Eq 1 & 2. We get,

CQ = CD.__________(3)

Since, AB || QP & AQ || BP

Therefore, ABPQ is a Parallelogram.

=> AB = QP._______(4)

Hence, From Eq 3 & 4. we get,

=> CQ = CD = QP.