Question

geometry unit 3 lesson 9 homework
name khloe augustine date 9 - 09 - 25 period 4
complete the two - column proof.
given: ∠tkf≅∠kfr
prove: ∠tkd≅∠wfg
statement reason
∠tkf≅∠kfr given
1.
2.
3.
4.
write the statements and reasons in the correct order in the two - column proof.
∠tkd≅∠gfr supplements of congruent angles are congruent.
∠tkd≅∠wfg if two angles form a linear pair, then they are supplementary.
tv∥wr if two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent.
∠gfr and ∠wfg are supplementary if alternate interior angles are congruent, then the two lines that are intersected by a transversal are parallel.

Explanation:

Step1: State parallel - line condition

$\angle TKF\cong\angle KFR$, so $TV\parallel WR$ (If alternate interior angles are congruent, then the two lines that are intersected by a transversal are parallel).

Step2: Use linear - pair property

$\angle TKD$ and $\angle TKF$ form a linear pair, so $\angle TKD+\angle TKF = 180^{\circ}$ (If two angles form a linear pair, then they are supplementary). Also, $\angle WFG$ and $\angle KFR$ form a linear pair, so $\angle WFG+\angle KFR=180^{\circ}$.

Step3: Apply congruent - supplements theorem

Since $\angle TKF\cong\angle KFR$, then $\angle TKD\cong\angle WFG$ (Supplements of congruent angles are congruent).

Answer:

Statement	Reason
$TV\parallel WR$	If alternate interior angles are congruent, then the two lines that are intersected by a transversal are parallel
$\angle TKD+\angle TKF = 180^{\circ}$, $\angle WFG+\angle KFR = 180^{\circ}$	If two angles form a linear pair, then they are supplementary
$\angle TKD\cong\angle WFG$	Supplements of congruent angles are congruent