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Questions and Answers
What does the Side-Side-Side Congruence Postulate (SSS) state?
What does the Side-Side-Side Congruence Postulate (SSS) state?
- If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then they are congruent.
- If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. (correct)
- If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then they are congruent.
- If three angles of one triangle are congruent to three angles of another triangle, then the triangles are congruent.
What does the Side-Angle-Side Congruence Postulate (SAS) state?
What does the Side-Angle-Side Congruence Postulate (SAS) state?
- If two angles and a nonincluded side of one triangle are congruent to the corresponding parts of another triangle, then they are congruent.
- If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. (correct)
- If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
- If two angles of a triangle are congruent to a corresponding pair of another triangle, then they are congruent.
What is the Angle-Side-Angle Congruence Postulate (ASA)?
What is the Angle-Side-Angle Congruence Postulate (ASA)?
If two angles and the included side are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Explain the Angle-Angle-Side Congruence Theorem (AAS).
Explain the Angle-Angle-Side Congruence Theorem (AAS).
What does the Hypotenuse-Leg Congruence Theorem (HL) state?
What does the Hypotenuse-Leg Congruence Theorem (HL) state?
What is the Angle Bisector Theorem?
What is the Angle Bisector Theorem?
Define the term Perpendicular Bisector.
Define the term Perpendicular Bisector.
What does the Perpendicular Bisector Theorem state?
What does the Perpendicular Bisector Theorem state?
Theorems to remember include the definition of ________ lines.
Theorems to remember include the definition of ________ lines.
The right angles theorem is important for defining ________ triangles.
The right angles theorem is important for defining ________ triangles.
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Study Notes
Congruent Triangles Postulates and Theorems
- Side-Side-Side Congruence Postulate (SSS): Triangles are congruent if all three corresponding sides are equal in measure.
- Side-Angle-Side Congruence Postulate (SAS): Triangles are congruent if two sides and the included angle of one triangle match with the two sides and included angle of another triangle.
- Angle-Side-Angle Congruence Postulate (ASA): Triangles are congruent if two angles and the included side of one triangle correspond to two angles and the included side of another triangle.
- Angle-Angle-Side Congruence Theorem (AAS): Triangles are congruent if two angles and a non-included side of one triangle align with two angles and the corresponding non-included side of another triangle.
- Hypotenuse-Leg Congruence Theorem (HL): For right triangles, congruence is established if the hypotenuse and one leg of one triangle are equal to the hypotenuse and leg of another right triangle.
Angle and Segment Theorems
- Angle Bisector Theorem: A point located on the bisector of an angle is equidistant from the two sides forming that angle.
- Perpendicular Bisector Definition: A perpendicular bisector is a line that intersects a segment at its midpoint and forms right angles to that segment.
- Perpendicular Bisector Theorem: A point on the perpendicular bisector of a segment is equidistant from the segment's endpoints.
Important Theorems to Remember
- Definition of perpendicular lines, which intersects at right angles.
- Right Angles Theorem: All right angles are congruent.
- Corresponding Angles Theorem: When two lines are cut by a transversal, the corresponding angles are equal.
- Definition of midpoint: A point that divides a segment into two equal parts.
- Vertical Angle Theorem: Vertical angles are congruent.
- Alternate Interior Angle Theorem: When two parallel lines are cut by a transversal, the alternate interior angles are congruent.
- Reflexive Property of Congruence: An object is congruent to itself.
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