Question

7.(b) 7. in fig. 12.10 ,

$$\begin{gathered} \angle 1\cong \angle 2and\angle 5\cong \angle 6. \\ \left(b\right)is\angle 7\cong \angle 8? \\ givereasoninsupportofyouranswer. \end{gathered}$$

Answer 1

step 1:- given:- $\angle 1\cong \angle 2and\angle 5\cong \angle 6.$

to proof :- $\angle 7\cong \angle 8$

step 2:-

$$\begin{gathered} IntriangleBCDandQRS \\ \angle 7={180}^0-\angle CBD-\angle 1and\angle 8={180}^0-\angle RQS-\angle 2 \\ soif\angle 1\cong \angle 2, \\ and\angle QSP\cong \angle BDA \\ \Rightarrow \angle CBD\cong \angle RSQ(alternateinteriorangle) \\ Nowiftwopairsofanglesoftwotrianglesarecongruentthenthird \\ pairofanglesisalsocongruent. \\ \Rightarrow \angle 7\cong \angle 8 \end{gathered}$$