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Q12

Expert-verifiedFound in: Page 42

Book edition
Student Edition

Author(s)
Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages
227 pages

ISBN
9780395977279

Copy everything shown and write a two-column proof.

Given: $RP=TQ;$

$PS=QS$

Prove: $RS=TS$

Statements | Reasons |

1. $\begin{array}{c}RP=TQ;\\ PS=QS\end{array}$ | Given |

2. $RP+PS=TQ+QS$ | 2. Addition property |

3. $\begin{array}{c}RS=RP+PS;\\ TS=TQ+QS\end{array}$ | 3. Segment addition postulate |

4. $RS=TS$ | 4. Substitution property |

If $a=b$ and $c=d$, then $a+c=b+d$.

$RP+PS=TQ+QS$

From the given figure, it can be observed that sum of $RP$ and $PS$ gives $RS$, that is $RS=RP+PS$.

From the given figure, it can be observed that sum of $TQ$ and $QS$ gives $TS$, that is $TS=TQ+QS$.

Substitute $RS$ for $RP+PS$ and $TS$ for $TQ+QS$ in step 1.

$\begin{array}{c}RP+PS=TQ+QS\\ RS=TS\end{array}$

Hence, it is proved that $RS=TS$.

Write a two-column proof with the help of the above-mentioned steps.

Statements | Reasons |

1. $\begin{array}{c}RP=TQ;\\ PS=QS\end{array}$ | Given |

2. $RP+PS=TQ+QS$ | 2. Addition property |

3. $\begin{array}{c}RS=RP+PS;\\ TS=TQ+QS\end{array}$ | 3. Segment addition postulate |

4. $RS=TS$ | 4. Substitution property |

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