Question

practice quiz: perimeter and circumference
look at this figure.
figure shows vertex y with two rays: one through point x (ray yx) and one through point z (ray yz), forming an angle at y
which of these can all be found on the figure?
○ point xz, ray y, angle xyz
○ point yz, ray yx, angle zyx
○ point y, ray yz, angle xyz
○ point z, ray xyz, angle xy

Explanation:

Step1: Analyze each option

• Option 1: "point XZ" is incorrect (a point is a single location, XZ would imply a segment or something else), "ray Y" is incorrect (a ray needs a starting point and a direction, just Y is a point).
• Option 2: "point YZ" is incorrect (YZ is a segment or ray, not a point), "ray YX" – let's check the figure, the ray from Y to X? Wait, the figure has ray YZ (horizontal) and ray YX (the other one). But "point YZ" is wrong.
• Option 3: "point Y" – Y is a vertex (point), "ray YZ" – the horizontal ray from Y through Z, "angle XYZ" – the angle at Y between rays YX and YZ. Let's verify: Y is a point, ray YZ exists (starts at Y, goes through Z), angle XYZ is the angle at Y between YX and YZ. This seems correct.
• Option 4: "ray XYZ" is incorrect (a ray has one starting point, XYZ is not a valid ray notation), "angle XY" is incorrect (an angle needs three points, with the middle being the vertex).

Step2: Confirm the correct option

After analyzing each part of the options, only Option 3 has all valid components: point Y (exists), ray YZ (exists as the horizontal ray from Y through Z), and angle XYZ (the angle at Y between YX and YZ).

Answer:

point Y, ray YZ, angle XYZ (the third option: point Y, ray YZ, angle XYZ)