Question
In triangles PQR and MST, $\angle\text{P}=55^\circ,\angle\text{Q}=25^\circ\angle{\text{M}}=100^\circ$ and $\angle{\text{S}}=25^\circ.$ Is $\triangle\text{QPR}\sim\triangle\text{TSM}?$ Why?
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Answer
False:$\triangle\text{QPR}$ and $\triangle\text{TSM}$ will be similar if its corresponding angles are equal $\angle\text{Q}=25^\circ$ $\angle\text{P}=55^\circ$ $\Rightarrow\angle\text{R}=180^\circ-(25^\circ+55^\circ)$ $\Rightarrow\angle{\text{R}}=180^\circ+80^\circ$ $\Rightarrow\angle{\text{R}}=100^\circ$ $\Rightarrow\angle{\text{S}}=25^\circ$ $\Rightarrow\angle{\text{M}}=100^\circ$ $\Rightarrow\angle\text{T}=180^\circ-(100^\circ+25^\circ)$ $\Rightarrow\angle\text{T}=55^\circ$ $\therefore\angle\text{Q}\neq\angle{\text{T}}$ $\angle\text{P}\neq\angle{\text{S}}$ $\angle\text{R}\neq\angle{\text{M}}$ So, $\triangle\text{QPR}$ is not similar to $\triangle\text{TSM}.$ So, the given statement $\triangle\text{QPR}\sim\triangle\text{TSM}$ is false.
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