Question

1. the figure is not in scale. select all the statements in the figure on the right side that you think are correct:

a. $\triangle kom \sim \triangle doc$

b. $\triangle lop \sim \triangle doc$

c. $lp \parallel dc$

d. $km \parallel dc$

Explanation:

Step1: Calculate ∠OKM in △KOM

In $\triangle KOM$, sum of angles is $180^\circ$.
$\angle OKM = 180^\circ - 64^\circ - 46^\circ = 70^\circ$

Step2: Calculate ∠ODC in △DOC

In $\triangle DOC$, $\angle DOC = 64^\circ$, $\angle OCD = 46^\circ$.
$\angle ODC = 180^\circ - 64^\circ - 46^\circ = 70^\circ$

Step3: Check △KOM ~ △DOC

$\angle KOM = \angle DOC$ (common angle), $\angle OKM = \angle ODC$, $\angle OMK = \angle OCD$. By AA similarity, $\triangle KOM \sim \triangle DOC$.

Step4: Check KM || DC

Corresponding angles $\angle OMK = \angle OCD = 46^\circ$, so $KM \parallel DC$.

Step5: Check ∠OLP in △LOP

$\angle OLP = 100^\circ$, $\angle ODC = 70^\circ$. These are not equal, so $LP$ is not parallel to $DC$, and $\triangle LOP
sim \triangle DOC$.

Answer:

A. $\Delta KOM \sim \Delta DOC$
D. $KM \parallel DC$