Question

7. In fig. 12.10,

$$\begin{gathered} \angle 1\cong \angle 2and\angle 5\cong \angle 6. \\ \left(a\right)is\angle 3\cong \angle 4? \\ givereasoninsupportofyouranswer. \end{gathered}$$

Answer 1

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

to proof :- $\angle 3\cong \angle 4$

step 2:-

$$\begin{gathered} \angle 2={180}^0-\angle QSPand\angle 1={180}^0-\angle BDA \\ soif\angle 1\cong \angle 2, \\ \Rightarrow {180}^0-\angle BDA\cong {180}^0-\angle QSP \\ \Rightarrow \angle BDA\cong \angle QSP \\ Nowiftwopairsofanglesoftwotrianglesarecongruentthenthird \\ pairofanglesisalsocongruent. \\ as\angle BDA\cong \angle QSPand\angle 5\cong \angle 6 \\ \Rightarrow \angle 3\cong \angle 4 \end{gathered}$$