Find lengths and measures of bisected lines and angles

Learning Objectives Identify and define segment bisectors and angle bisectors. Apply the definition of a midpoint to find unknown segment lengths. Apply the definition of an angle bisector to find unknown angle measures. Set up and solve linear equations to determine lengths of bisected segments. Set up and solve linear equations to determine measures of bisected angles. Calculate the total length of a bisected segment or the total measure of a bisected angle. Ever wondered how a perfectly cut pizza slice or a precisely folded piece of paper ensures equal halves? 🍕📐 It's all about bisection! In this lesson, you'll learn how to identify and work with bisected lines and angles. Understanding bisection is crucial for solving geometric problems and lays the groundwo...

TermDefinitionExample Line SegmentA part of a line that is bounded by two distinct endpoints. It has a definite length.If you draw a line from point A to point B, that's a line segment, often written as $\overline{AB}$. AngleFormed by two rays (sides) sharing a common endpoint (vertex). It is measured in degrees.The corner of a square is a 90-degree angle, often written as $\angle ABC$. MidpointThe point that divides a line segment into two congruent (equal in length) segments.If M is the midpoint of $\overline{AB}$, then $\overline{AM}$ and $\overline{MB}$ have the same length. Segment BisectorA line, ray, segment, or plane that intersects a line segment at its midpoint, dividing it into two congruent segments.A line 'l' passing through the midpoint M of $\overline{PQ}$ is...

Midpoint Rule for Segments If point M is the midpoint of segment $\overline{AB}$, then $AM = MB$. This rule states that a midpoint divides a segment into two equal parts. You can use this to set up an equation if you have algebraic expressions for the lengths of the two parts. Segment Bisector Rule If line 'l' bisects segment $\overline{AB}$ at point M, then $AM = MB$ and $AB = AM + MB = 2 \cdot AM = 2 \cdot MB$. This rule extends the midpoint concept. Not only are the two parts equal, but the total length of the segment is twice the length of one of its bisected parts. Use this to find the total length after finding the individual parts. Angle Bisector Rule If ray $\overrightarrow{BD}$ bisects $\angle ABC$, then $m\angle ABD = m\angle DBC$. This rule means...