To determine:To prove:The congruency of /_PBC ~=/_PBD. Given information: The following information has been given /_BPC=/_BPD=90^(circ) /_C=/_D

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asked 2020-12-29
To determine:To prove:The congruency of \(\displaystyle\angle{P}{B}{C}\stackrel{\sim}{=}\angle{P}{B}{D}\).
Given information:
The following information has been given
\(\displaystyle\angle{B}{P}{C}=\angle{B}{P}{D}={90}^{{\circ}}\)
\(\displaystyle\angle{C}=\angle{D}\)

Answers (1)

2020-12-30
Formula used : If any two triangles have two common angles, then by virtue of similarity, third angle will also be congruent
Proof : In triangles PBC and PBD, we have
\(\displaystyle\angle{B}{P}{C}=\angle{B}{P}{D}={90}^{{\circ}}\)
\(\displaystyle\angle{C}=\angle{D}\)
Thus, by virtue of similarity, third angle will also be congruent. Hence,
\(\displaystyle\angle{P}{B}{C}\stackrel{\sim}{=}\angle{P}{B}{D}\)
Thus, the given congruency is proved
0

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