10 Questions
What is the sum of the interior angles of a triangle?
180°
What is the measure of an exterior angle of a triangle equal to?
The sum of the measures of its remote interior angles.
What is required for SSS congruence?
Three sides of one triangle equal to three sides of another triangle
What is true about a parallelogram?
Its diagonals bisect each other.
What is the sum of the interior angles of a quadrilateral?
360°
What is required for SAS congruence?
Two sides and the included angle
What is true about opposite sides of a parallelogram?
They are parallel.
What is required for ASA congruence?
Two angles and the included side
What is true about opposite angles of a parallelogram?
They are congruent.
What is required for AAS congruence?
Two angles and a non-included side
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
-
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.
Test your knowledge of Euclidean geometry, covering key properties and concepts of triangles, congruent triangles, quadrilaterals, and their various types.
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