can you guys please please help me with question 14 in the photo.. please help me
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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.
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.
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3
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.
☆ 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.
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