2 Answers

Popgalop · Answer 1 · 2024-12-18T13:22:22+0000

Final answer:

The student's question is about the missing statement from a proof plan for constructing an angle bisector in geometry, but the information provided as an example pertains to vector components in physics. The proper steps for angle bisector construction in geometry would be the relevant part of the explanation.

Step-by-step explanation:

The student is asking for help in identifying the missing statement from a proof plan for constructing an angle bisector. In geometry, an angle bisector is a line or ray that divides an angle into two equal parts. While the question pertains to the steps in a proof for constructing an angle bisector, the example provided is related to vector components in physics, specifically mentioning how vectors Ax and Ay combine to form vector A in a right triangle. This example serves to explain the concept of vector components but is not directly related to angle bisectors in geometry. To help with the missing proof statement, it's important to know the typical steps involved in constructing an angle bisector: drawing a circle centered at the vertex of the angle, finding two points where the circle intersects the angle's legs, and then drawing a new line from the vertex through the midpoint of the arc connecting those two points on the circle.

Darshan Sawardekar · Answer 2 · 2024-12-19T22:53:09+0000

Since Sawyer is writing a proof for his construction of an angle bisector, a statement that is missing from his plan is: b) HA = HB and AL = BL.

In Mathematics and Euclidean Geometry, an angle bisector is a type of line, ray, or segment, that typically divides or bisects a line segment exactly into two (2) equal and congruent angles.

Based on the definition of angle bisector, we can logically deduce the following angle measures;

Statement Reasons

HA = HB and AL = BL Radii of constructed arc are same length.

LH = LH Reflexive property

ΔHBL ≅ ΔHAL SSS Congruence property

m∠AHL ≅ m∠BHL Corresponding angles of congruent triangles.

In conclusioon, HA = HB and AL = BL because the radii of constructed arc have the same length, and point L is equidistant to A and M.