Question

click the arrows to choose an answer from each menu. if $overline{xz}$ and $overline{yz}$ are drawn on the construction from step 3, lengths $kx = ky$ and $xz=$ choose... since they are choose.... in addition, $overline{kz}cong$ choose... by the reflexive property of congruence. so, $\triangle kxzcong$ choose... by the side - side - side (sss) postulate and $angle jkzcongangle lkz$ since they are corresponding parts of congruent triangles.

Explanation:

Step1: Analyze construction

In the construction, when arcs are drawn with the same compass - setting, the lengths of the radii of the arcs are equal. Since the arcs are drawn from the same center \(K\) to intersect the sides of the angle at \(X\) and \(Y\), \(KX = KY\). Also, when the second set of arcs are drawn from \(X\) and \(Y\) to intersect at \(Z\), \(XZ=YZ\) because they are the radii of congruent arcs (drawn with the same compass - setting).

Step2: Consider congruence property

\(\overline{KZ}\cong\overline{KZ}\) by the Reflexive Property of Congruence.

Step3: Apply SSS postulate

In \(\triangle KXZ\) and \(\triangle KYZ\), we have \(KX = KY\), \(XZ = YZ\), and \(KZ=KZ\). So, \(\triangle KXZ\cong\triangle KYZ\) by the Side - Side - Side (SSS) postulate.

Answer:

1. \(YZ\), radii of congruent arcs
2. \(\overline{KZ}\), Reflexive Property of Congruence
3. \(\triangle KYZ\), SSS postulate