26. Complete the following proof. Given: ∠ QPS ≅∠ TPR Prove:...

26. Complete the following proof. Given: $\angle QPS \cong \angle TPR$ Prove: $\angle QPR \cong \angle TPS$ Proof: Statements Reasons a. a. b. $m\angle QPS = m\angle TPR$ b. c. $m\angle QPS = m\angle QPR + m\angle RPS$ $m\angle TPR = m\angle TPS + m\angle RPS$ c. d. d. Substitution e. e. f. f. continued

Use the given paragraph proof to write a two-column proof Given: $\angle 1 \cong \angle 4$ Prove: $\angle 2$ and $\angle 3$ are supplementary. Paragraph proof: $\angle 4$ and $\angle 3$ form a linear pair, so they are supplementary by the Linear Pair Theorem. Therefore, $m \angle 4+m \angle 3=180^{\circ} .$ Also, $\angle 1$ and $\angle 2$ are vertical angles, so $\angle 1 \cong \angle 2$ by the Vertical Angles Theorem. It is given that $\angle 1 \cong \angle 4 .$ So by the Transitive Property of Congruence, $\angle 4 \cong \angle 2,$ and by the definition of congruent angles, $\mathrm{m} \angle 4=\mathrm{m} \angle 2 .$ By substitution, $\mathrm{m} \angle 2+\mathrm{m} \angle 3=180^{\circ},$ so $\angle 2$ and $\angle 3$ are supplementary by the definition of supplementary angles. CAN'T COPY THE FIGURE

Geometric Reasoning

Flowchart and Paragraph Proofs

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