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Questions and Answers
What is the sum of the interior angles of a triangle?
What is the sum of the interior angles of a triangle?
What is the measure of an exterior angle of a triangle equal to?
What is the measure of an exterior angle of a triangle equal to?
What is required for SSS congruence?
What is required for SSS congruence?
What is true about a parallelogram?
What is true about a parallelogram?
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What is the sum of the interior angles of a quadrilateral?
What is the sum of the interior angles of a quadrilateral?
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What is required for SAS congruence?
What is required for SAS congruence?
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What is true about opposite sides of a parallelogram?
What is true about opposite sides of a parallelogram?
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What is required for ASA congruence?
What is required for ASA congruence?
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What is true about opposite angles of a parallelogram?
What is true about opposite angles of a parallelogram?
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What is required for AAS congruence?
What is required for AAS congruence?
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Study Notes
Triangles and Congruence
Properties of Triangles
- Angle Sum Property: The sum of the interior angles of a triangle is always 180°.
- Exterior Angle Property: The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Congruent Triangles
- SSS (Side-Side-Side) Congruence: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.
- SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.
- ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
- AAS (Angle-Angle-Side) Congruence: If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
Quadrilaterals
Properties of Quadrilaterals
- Sum of Interior Angles: The sum of the interior angles of a quadrilateral is always 360°.
- Diagonals: The diagonals of a quadrilateral bisect each other if and only if it is a parallelogram.
Types of Quadrilaterals
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Parallelogram: A quadrilateral with opposite sides that are parallel.
- Opposite sides are equal in length.
- Opposite angles are equal.
- Rectangle: A parallelogram with four right angles.
- Rhombus: A parallelogram with all sides of equal length.
- Square: A rectangle with all sides of equal length.
- Trapezoid: A quadrilateral with at least one pair of opposite sides that are not parallel.
Note: These notes provide a concise overview of key concepts in Euclidean Geometry, focusing on triangles and congruence, as well as quadrilaterals.
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Description
Test your knowledge of Euclidean geometry, covering key properties and concepts of triangles, congruent triangles, quadrilaterals, and their various types.
