Mathematics
Grade 10
15 min
Find lengths and measures of bisected lines and angles
Find lengths and measures of bisected lines and angles
What you'll learn
- Identify bisected lines and angles in geometric figures with 80% accuracy.
- Apply the definition of a bisector to calculate the length of line segments after bisection, achieving correct answers in 4 out of 5 problems.
- Solve for unknown angle measures created by an angle bisector, demonstrating proficiency by correctly solving at least 70% of the assigned practice problems.
- Explain, in writing, the relationship between a bisector and the original line segment or angle, using appropriate mathematical vocabulary, in at least 3 out of 4 opportunities.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define segment bisectors, midpoints, and angle bisectors.
Set up and solve algebraic equations based on the properties of bisected segments.
Set up and solve algebraic equations based on the properties of bisected angles.
Calculate the total length of a segment or measure of an angle using the value of a variable found from its bisected parts.
Apply the concept of bisection to problems involving congruent triangles.
Differentiate between a bisector and a perpendicular bisector.
Use bisection properties as justifications in geometric proofs.
How does a carpenter find the exact center of a wooden beam to ensure perfect balance? 🪚 They use the same geometric principle you're about to master: bisection!
This tutorial will teach you how to work with l...
2
Key Concepts & Vocabulary
TermDefinitionExample
BisectTo divide a geometric figure, such as a line segment or an angle, into two congruent (equal) parts.If you cut a 10 cm rope exactly in the middle, you have bisected it into two 5 cm pieces.
Segment BisectorA point, line, ray, or segment that intersects another segment at its midpoint, dividing it into two congruent segments.In segment \overline{AC}, if point B is the midpoint, then line \overleftrightarrow{DB} is a segment bisector of \overline{AC}.
MidpointThe point on a line segment that divides it into two segments of equal length. It is the point of bisection.If M is the midpoint of \overline{PQ}, and PQ = 12, then PM = 6 and MQ = 6.
Angle BisectorA ray that originates from the vertex of an angle and divides it into two adjacent, congruent angles.If ray \ove...
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Core Formulas
Definition of a Segment Bisector
If a point, line, ray, or segment bisects \overline{AB} at point M, then \overline{AM} \cong \overline{MB}. This implies that AM = MB.
Use this rule when you are given that a segment is bisected. Set the lengths of the two smaller, equal parts equal to each other to solve for unknown values. The total length AB = 2 * AM or AB = 2 * MB.
Definition of an Angle Bisector
If ray \overrightarrow{BX} bisects \angle ABC, then \angle ABX \cong \angle XBC. This implies that m\angle ABX = m\angle XBC.
Use this rule when you are given that an angle is bisected. Set the measures of the two smaller, equal angles equal to each other to solve for unknown values. The total angle measure m\angle ABC = 2 * m\angle ABX or m\angle ABC = 2 * m\angle XBC.
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Sign Up Free to ContinueSample Practice Questions
Easy
What is the specific name for a point on a line segment that divides it into two segments of equal length?
A.Vertex
B.Endpoint
C.Midpoint
D.Origin
Easy
If ray \(\overrightarrow{BD}\) is an angle bisector of \(\angle ABC\), which of the following statements must be true?
A.\(m\angle ABD = m\angle ABC\)
B.\(m\angle DBC = \frac{1}{2} m\angle ABC\)
C.\(m\angle ABC = \frac{1}{2} m\angle DBC\)
D.\(\overrightarrow{BD} \perp \overline{AC}\)
Easy
Point M is the midpoint of segment \(\overline{PQ}\). If the length of \(\overline{PM}\) is 12 cm, what is the length of \(\overline{PQ}\)?
A.6 cm
B.12 cm
C.18 cm
D.24 cm
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What grade level is "Find lengths and measures of bisected lines and angles"?
Find lengths and measures of bisected lines and angles is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Find lengths and measures of bisected lines and angles?
You'll be able to: Identify bisected lines and angles in geometric figures with 80% accuracy; Apply the definition of a bisector to calculate the length of line segments after bisection, achieving correct answers in 4 out of 5 problems; Solve for….
Is "Find lengths and measures of bisected lines and angles" free to practice?
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How many practice questions are included with Find lengths and measures of bisected lines and angles?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.