Question

1. a diagram is shown. a. select all of the statements that are true. □∠drh≅∠krc □∠hrc≅∠krd □∠mkp≅∠bkn □∠nkb≅∠rkp □∠rdk≅∠rkd □∠wdy≅∠rdk

Explanation:

Step1: Recall vertical - angle property

Vertical angles are congruent. $\angle DRH$ and $\angle KRC$ are vertical angles, so $\angle DRH\cong\angle KRC$.

Step2: Analyze another pair of vertical angles

$\angle HRC$ and $\angle KRD$ are vertical angles, so $\angle HRC\cong\angle KRD$.

Step3: Check right - angle congruence

$\angle MKP$ and $\angle BKN$ are both right angles (since $\angle MKN = 90^{\circ}$ and they are formed by the intersection of lines), so $\angle MKP\cong\angle BKN$.

Step4: Analyze non - congruent angles

$\angle NKB$ and $\angle RKP$ are not vertical angles and there is no information to suggest they are congruent. $\angle RDK$ and $\angle RKD$ are angles in a triangle and are not generally congruent. $\angle WDY$ and $\angle RDK$ are vertical angles, so $\angle WDY\cong\angle RDK$.

Answer:

$\angle DRH\cong\angle KRC$, $\angle HRC\cong\angle KRD$, $\angle MKP\cong\angle BKN$, $\angle WDY\cong\angle RDK$