CONGRUENT LINE SEGMENTS I MATHEMATICS 3 QUARTER 3 MELC 38 I DEPED MELC-BASED - Free Printable

The image you uploaded is related to a mathematics lesson, specifically focusing on Quarter 3 MELC 38, which involves demonstrating and identifying congruent line segments. Below, I will explain the concept of congruent line segments and provide a solution or explanation for how to identify them.

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Understanding Congruent Line Segments

1. Definition:
- Two line segments are congruent if they have the same length.
- In mathematical notation, if line segment \( AB \) is congruent to line segment \( CD \), we write it as:
\[
AB \cong CD
\]

2. Key Points:
- Congruence is denoted by the symbol \( \cong \).
- To determine if two line segments are congruent, their lengths must be equal.
- Congruence does not depend on the orientation or position of the line segments; only their lengths matter.

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How to Identify Congruent Line Segments

There are several methods to identify whether two line segments are congruent:

#### 1. Measurement Method
- Use a ruler or measuring tool to measure the lengths of both line segments.
- If the lengths are equal, the line segments are congruent.
- Example:
- Measure \( AB \) and find its length to be 5 cm.
- Measure \( CD \) and find its length to be 5 cm.
- Since both lengths are equal, \( AB \cong CD \).

#### 2. Using a Compass
- Place the compass point on one endpoint of the first line segment (e.g., \( A \)) and adjust the compass so that the pencil tip touches the other endpoint (e.g., \( B \)).
- Without changing the compass setting, place the compass point on one endpoint of the second line segment (e.g., \( C \)) and draw an arc.
- If the arc passes through the other endpoint (e.g., \( D \)), then the two line segments are congruent.

#### 3. Geometric Construction
- In geometric diagrams, congruent line segments are often marked with small tick marks or arcs.
- For example:
- If line segment \( AB \) has one tick mark and line segment \( CD \) also has one tick mark, they are congruent.
- Similarly, if both segments are labeled with the same measurement (e.g., 5 cm), they are congruent.

#### 4. Using Coordinate Geometry
- If the coordinates of the endpoints of the line segments are given, use the distance formula to calculate their lengths.
- The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
\text{Length} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
- Compare the calculated lengths to determine congruence.

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Example Problem

Suppose you are given two line segments:
- Line segment \( PQ \) with endpoints \( P(1, 2) \) and \( Q(4, 6) \).
- Line segment \( RS \) with endpoints \( R(3, 5) \) and \( S(6, 9) \).

Task: Determine if \( PQ \) and \( RS \) are congruent.

Solution:
1. Calculate the length of \( PQ \) using the distance formula:
\[
PQ = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]

2. Calculate the length of \( RS \) using the distance formula:
\[
RS = \sqrt{(6 - 3)^2 + (9 - 5)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]

3. Compare the lengths:
- Length of \( PQ \) = 5
- Length of \( RS \) = 5
- Since both lengths are equal, \( PQ \cong RS \).

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Final Answer

\[
\boxed{PQ \cong RS}
\]

This method can be applied to any problem involving the identification of congruent line segments. If you have a specific problem or diagram, feel free to share it, and I can provide a more detailed solution!