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Q1.

Expert-verifiedFound in: Page 129

Book edition
Student Edition

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

Pages
227 pages

ISBN
9780395977279

**Describe your plan for proving the following.**

**1. Given: $\overline{\mathbf{P}\mathbf{R}}$ bisects $\mathbf{\angle}\mathit{Q}\mathit{P}\mathit{S}\mathbf{;}\mathbf{\text{}}\overline{\mathbf{P}\mathbf{Q}}\mathbf{\cong}\overline{\mathbf{P}\mathbf{S}}$ Prove: ** $\mathbf{\angle}\mathit{Q}\mathbf{\cong}\mathbf{\angle}\mathit{S}$

$\overline{PR}\cong \overline{PR}$ (reflexive property)

$\angle QPR\cong \angle SPR$ (bisector of an angle divides it into congruent angles)

$\Delta PQR\cong \Delta SPR$ (SAS congruence criteria)

$\angle Q\cong \angle S$ (corresponding parts of congruent triangles)

According to reflexive property of congruence, a line segment is congruent to itself.

As bisector of an angle divides it into congruent angles

According to SAS congruence criteria, two triangles are said to be congruent if two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle

So, from step 1, step 2 and using given

$\Delta PQR\cong \Delta SPR$

As corresponding parts of congruent triangles are equal

Hence, $\angle Q\cong \angle S$

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