Mathematics
Grade 10
15 min
Perpendicular Bisector Theorem
Perpendicular Bisector Theorem
What you'll learn
- Identify pairs of whole numbers within 100 that have a sum of a given target number, and accurately list at least 3 different pairs.
- Solve subtraction problems involving two-digit numbers to find the difference, and then identify another set of two-digit numbers with the same difference, achieving 80% accuracy.
- Explain the relationship between addition and subtraction, using examples of number pairs with a specific sum or difference.
- Apply the concept of inverse operations (addition and subtraction) to find missing numbers in equations with a target sum or difference, solving correctly in at least 4 out of 5 problems.
Tutorial Preview
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Introduction & Learning Objectives
Learning Objectives
Define a perpendicular bisector and its properties.
State and explain the Perpendicular Bisector Theorem.
State and explain the Converse of the Perpendicular Bisector Theorem.
Apply the theorem and its converse to solve for unknown lengths and variables in geometric figures.
Prove the Perpendicular Bisector Theorem using triangle congruence postulates.
Determine if a point lies on a perpendicular bisector by applying the converse of the theorem.
Imagine you and a friend are standing in a field. Where could a third person stand so they are the exact same distance from both of you? 🤔
This tutorial explores the Perpendicular Bisector Theorem, a fundamental rule in geometry that connects points, distances, and lines. You will learn the theorem, its converse...
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Key Concepts & Vocabulary
TermDefinitionExample
Perpendicular BisectorA line, ray, or segment that intersects another segment at its midpoint and forms a 90° angle.If line 'l' passes through the midpoint M of segment AB and l ⊥ AB, then 'l' is the perpendicular bisector of AB.
EquidistantBeing at an equal distance from two or more points.If the distance from point C to point A is 5 cm, and the distance from point C to point B is also 5 cm, then C is equidistant from A and B.
MidpointThe point on a line segment that divides it into two congruent (equal length) segments.If M is the midpoint of segment XY, then XM = MY.
Perpendicular LinesTwo lines that intersect to form a right angle (90°).The x-axis and y-axis on a Cartesian plane are perpendicular lines.
Congruent SegmentsLine segments that hav...
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Core Formulas
Perpendicular Bisector Theorem
If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Use this theorem when you are GIVEN that a line is a perpendicular bisector and you need to prove or find the lengths of the segments connecting a point on that line to the endpoints. If line 'l' is the perpendicular bisector of segment AB and point P is on 'l', then PA = PB.
Converse of the Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.
Use this theorem when you are GIVEN that a point is equidistant from a segment's endpoints and you need to prove that the point lies on the perpendicular bisector. If PA...
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Challenging
What is the equation of the perpendicular bisector of the segment with endpoints A(-2, 1) and B(4, 5)?
A.y = -3/2x + 9/2
B.y = 2/3x + 7/3
C.y = -3/2x + 3
D.y = 2/3x + 3
Challenging
In isosceles triangle ΔXYZ with base YZ, the altitude from vertex X to the base is drawn, meeting the base at M. Why is this altitude XM guaranteed to be the perpendicular bisector of YZ?
A.By definition, an altitude is always a perpendicular bisector.
B.Because ΔXYZ is isosceles, XY = XZ, making point X equidistant from Y and Z. The Converse of the Perpendicular Bisector Theorem applies.
C.The Perpendicular Bisector Theorem states that any line from a vertex to the opposite side is a perpendicular bisector.
D.This can only be proven using the Pythagorean theorem.
Challenging
In ΔABC, the perpendicular bisector of side AB and the perpendicular bisector of side BC intersect at a point P. Which of the following statements must be true?
A.P is the midpoint of AC.
B.PA = PB and PB = PC, therefore PA = PC.
C.Triangle ABC must be a right triangle.
D.Point P lies on side AC.
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Frequently asked questions
What grade level is "Perpendicular Bisector Theorem"?
Perpendicular Bisector Theorem is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Perpendicular Bisector Theorem?
You'll be able to: Identify pairs of whole numbers within 100 that have a sum of a given target number, and accurately list at least 3 different pairs; Solve subtraction problems involving two-digit numbers to find the difference, and then….
Is "Perpendicular Bisector Theorem" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Perpendicular Bisector Theorem?
This lesson includes 40 practice questions across multiple difficulty levels, each with instant feedback and explanations.