Mathematics
Grade 10
15 min
Congruent line segments
Congruent line segments
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1
Introduction & Learning Objectives
Learning Objectives
Define congruent line segments and distinguish between congruence (≅) and equality (=).
Determine if line segments are congruent by calculating their lengths on a number line and in the coordinate plane.
Apply the definition of a midpoint and the Midpoint Theorem to prove segments are congruent.
Use the Segment Addition Postulate in conjunction with congruent segments to solve for unknown lengths.
Incorporate the concept of congruent segments as reasons in formal geometric proofs.
Construct a line segment congruent to a given line segment using a compass and straightedge.
Ever wonder how manufacturers produce millions of identical phone screens or car parts? ⚙️ The secret lies in a core geometric concept: congruence!
In this tutorial, you will learn the...
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Key Concepts & Vocabulary
TermDefinitionExample
Line SegmentA part of a line that is bounded by two distinct endpoints and contains every point on the line between its endpoints. It is denoted by its endpoints, such as \(\overline{AB}\).The edge of a ruler from the 0 cm mark to the 5 cm mark is a line segment.
Length of a SegmentThe distance between the endpoints of a line segment. The length of \(\overline{AB}\) is a positive number denoted as AB.If segment \(\overline{AB}\) spans from x=2 to x=7 on a number line, its length, AB, is 5 units.
Congruent Line SegmentsTwo or more line segments that have the exact same length. The symbol for congruence is ≅.If \(\overline{AB}\) is 10 cm long and \(\overline{CD}\) is 10 cm long, then \(\overline{AB} \cong \overline{CD}\).
Midpoint of a SegmentThe point on a line segmen...
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Core Formulas
Definition of Congruent Segments
Line segment \(\overline{AB}\) is congruent to line segment \(\overline{CD}\) if and only if their lengths are equal. Symbolically: \(\overline{AB} \cong \overline{CD} \iff AB = CD\)
This is the fundamental link between the geometric concept of congruence (≅) and the algebraic concept of equality (=). Use it to switch between statements about segments and statements about their lengths in proofs and problem-solving.
Distance Formula
The distance, d, (or length of a segment) between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a coordinate plane is given by: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Use this formula to calculate the length of a line segment when you are given the coordinates of its endpoints. You can then compare lengths...
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Sign Up Free to ContinueSample Practice Questions
Easy
Which statement provides the most accurate definition of congruent line segments?
A.Two line segments that are parallel to each other.
B.Two line segments that lie on the same line.
C.Two line segments that have the exact same length.
D.Two line segments that share a common endpoint.
Easy
Which of the following statements correctly uses the symbols for congruence (≅) and equality (=)?
A.If the length of segment AB is 5, we write \(\overline{AB} = 5\).
B.If segments \(\overline{AB}\) and \(\overline{CD}\) have the same length, we write \(\overline{AB} \cong \overline{CD}\).
C.If the length of segment AB equals the length of segment CD, we write \(AB \cong CD\).
D.If two segments are congruent, we can write \(\overline{AB} = \overline{CD}\).
Easy
If M is the midpoint of \(\overline{XY}\), which of the following must be true according to the Midpoint Theorem?
A.\(\overline{XM} \cong \overline{MY}\)
B.XM = 2 * XY
C.\(\overline{XY} \cong \overline{MY}\)
D.M is between X and Y, but the segments are not necessarily congruent.
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