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Questions and Answers
What is the condition for two triangles to be congruent by SAS?
What is the condition for two triangles to be congruent by SAS?
What is the main difference between congruence and equality?
What is the main difference between congruence and equality?
What is an example of congruent figures in real life?
What is an example of congruent figures in real life?
What is the condition for two triangles to be congruent by HL?
What is the condition for two triangles to be congruent by HL?
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What can be said about the two triangles in the image?
What can be said about the two triangles in the image?
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What is the condition for two shapes to be congruent?
What is the condition for two shapes to be congruent?
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Which of the following transformations does not affect the congruency of two shapes?
Which of the following transformations does not affect the congruency of two shapes?
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What can be concluded about two similar triangles that are not congruent?
What can be concluded about two similar triangles that are not congruent?
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Which criterion is used to determine congruence of two triangles?
Which criterion is used to determine congruence of two triangles?
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What is the relationship between congruent and similar shapes?
What is the relationship between congruent and similar shapes?
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Study Notes
Congruent Figures in Geometry
- Two figures are congruent if they have the same shape and size, despite possible differences in position and orientation.
- Congruent shapes have sides of the same length and angles of the same measure.
Transformations and Congruence
- Translation: a shape can be slid to change its position without affecting its congruence.
- Rotation: a shape can be turned at any angle without affecting its congruence.
- Reflection: a shape can be flipped without affecting its congruence.
Similarity vs Congruence
- Similar shapes have the same angles but may have different sizes.
- Congruent shapes are always similar, but similar shapes are not always congruent.
- Resizing a similar shape can make it congruent.
Determining Congruent Triangles
- SSS (Side-Side-Side): if all corresponding sides of two triangles are congruent, then the triangles are congruent.
- SAS (Side-Angle-Side): if a pair of sides and the angle between them are congruent, then the triangles are congruent.
- ASA (Angle-Side-Angle): if a pair of angles and the side between them are congruent, then the triangles are congruent.
- AAS (Angle-Angle-Side): if a pair of angles and a side (not between the angles) are congruent, then the triangles are congruent.
- HL (Hypotenuse-Leg): for right-angle triangles only, if the hypotenuse and corresponding legs are congruent, then the triangles are congruent.
Examples of Congruent Figures
- Congruent figures can be transformed in relation to each other through translation, rotation, or reflection.
- Congruent figures can be found in real-life applications, such as construction, where identical shapes and sizes are required.
Congruence vs Equality
- Congruence and equality are not interchangeable terms in mathematics.
- Equality implies that all properties are equal, while congruence accepts differences in position.
Incongruent Figures
- Incongruent figures have different shapes and sizes, and their pairs of sides and angles are not equal.
- Incongruent figures cannot be made congruent by resizing or transforming them.
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Description
Learn about congruent shapes, their definition, and properties in geometry. Discover what makes two shapes congruent, including equal sides and angles.
