Question

prove that ∠jkz≅∠lkz as a result of the construction. use the drop - down menus to complete the proof. step 1: set the compass width between k and j. draw arc xy through ∠jkl. step 2: keeping the compass width, draw arcs from x and y inside the angle. label the intersection z. step 3: use the straightedge to connect k and z. click the arrows to choose an answer from each menu. if xz and yz are drawn on the construction from step 3, lengths kx = ky and xz = choose... since they are choose.... in addition, kz≅ choose... by the reflexive property of congruence. so, △kxz≅ choose... by the ) postulate and ∠jkz≅∠lkz since they are corresponding parts of congruent

Explanation:

Step1: Analyze construction - equal radii

In the construction, when we set the compass width between \(K\) and \(J\) and draw arcs, \(KX = KY\) (radii of the same - arc). Also, when we draw the second - set of arcs with the same compass width, \(XZ=YZ\) since they are radii of congruent arcs.

Step2: Identify congruent sides

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

Step3: Apply congruence postulate

In \(\triangle KXZ\) and \(\triangle KYZ\), we have \(KX = KY\), \(XZ = YZ\), and \(KZ=KZ\). So, \(\triangle KXZ\cong\triangle KYZ\) by the SSS (Side - Side - Side) postulate. Since \(\angle J KZ\) and \(\angle LKZ\) are corresponding parts of congruent triangles \(\triangle KXZ\) and \(\triangle KYZ\), \(\angle J KZ\cong\angle LKZ\).

Answer:

If \(\overline{XZ}\) and \(\overline{YZ}\) are drawn on the construction from Step 3, lengths \(KX = KY\) and \(XZ = YZ\) since they are radii of congruent arcs. In addition, \(\overline{KZ}\cong\overline{KZ}\) by the Reflexive Property of Congruence. So, \(\triangle KXZ\cong\triangle KYZ\) by the SSS postulate and \(\angle J KZ\cong\angle LKZ\) since they are corresponding parts of congruent triangles.