Triangle Congruence Theorems Quiz
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Questions and Answers

What does CPCTC stand for?

Corresponding parts of congruent triangles are congruent.

What are congruent sides?

Sides that have the exact same length.

What is the Angle Side Angle (ASA) Postulate?

If two triangles have corresponding angles and included sides that are congruent, then the triangles themselves are congruent.

What does the Side Side Side (SSS) Postulate state?

<p>If two triangles have corresponding sides that are congruent, then the triangles are congruent.</p> Signup and view all the answers

What is the Angle Angle Side (AAS) Postulate?

<p>If two triangles have corresponding angles and a non-included side that are congruent, then the triangles are congruent.</p> Signup and view all the answers

What is the Hypotenuse Leg (HL) Postulate?

<p>If two right triangles have a corresponding side and hypotenuse that are congruent, then the triangles are congruent.</p> Signup and view all the answers

What does the Side Angle Side (SAS) Postulate assert?

<p>If two triangles have corresponding sides and included angles that are congruent, then the triangles are congruent.</p> Signup and view all the answers

What are corresponding sides?

<p>Sides that have the same relative positions in geometric figures.</p> Signup and view all the answers

What are corresponding angles?

<p>Angles that have the same relative positions in geometric figures.</p> Signup and view all the answers

What does the Third Angles Theorem state?

<p>If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent.</p> Signup and view all the answers

What is the Isosceles Triangle Theorem?

<p>If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent.</p> Signup and view all the answers

What is the Converse of the Isosceles Triangle Theorem?

<p>If 2 angles of a triangle are congruent, then the sides opposite of the angles are congruent.</p> Signup and view all the answers

What are congruent figures?

<p>Geometric figures that have the same shape and size.</p> Signup and view all the answers

What is an included side in a triangle?

<p>A side that is between two angles in a triangle.</p> Signup and view all the answers

What is an included angle in a triangle?

<p>An angle that is between two sides in a triangle.</p> Signup and view all the answers

Angle-Angle-Angle (AAA) proves triangles congruent.

<p>False</p> Signup and view all the answers

Side-Side-Angle (SSA) proves triangles congruent.

<p>False</p> Signup and view all the answers

What is an acute triangle?

<p>A triangle that has three acute angles.</p> Signup and view all the answers

What is an obtuse triangle?

<p>A triangle with one angle that measures greater than 90 degrees.</p> Signup and view all the answers

What is a right triangle?

<p>A triangle that has one angle whose measure is exactly 90 degrees.</p> Signup and view all the answers

What is an equiangular triangle?

<p>A triangle whose angles are all congruent.</p> Signup and view all the answers

What is a scalene triangle?

<p>A triangle that has no congruent sides.</p> Signup and view all the answers

What is an isosceles triangle?

<p>A triangle with at least two congruent sides.</p> Signup and view all the answers

What is an equilateral triangle?

<p>A triangle that has all three sides congruent.</p> Signup and view all the answers

What does the Triangle Sum Theorem state?

<p>The sum of the measures in a triangle is 180 degrees.</p> Signup and view all the answers

What does the Exterior Angle Theorem state?

<p>The sum of the remote interior angles is equal to the measure of the exterior angle.</p> Signup and view all the answers

What are congruent triangles?

<p>Triangles that have the same shape and size, all corresponding sides and angles are congruent.</p> Signup and view all the answers

What does CPCTC stand for?

<p>Corresponding parts of congruent triangles are congruent.</p> Signup and view all the answers

What is the Reflexive Property of Congruence?

<p>Segment DE is congruent to segment DE.</p> Signup and view all the answers

What does the Symmetric Property state?

<p>If segment DE is congruent to segment FG, then segment FG is congruent to segment DE.</p> Signup and view all the answers

What is the Transitive Property?

<p>If AB = CD and CD = EF, then AB = EF.</p> Signup and view all the answers

Study Notes

Triangle Congruence Theorems and Properties

  • CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that all corresponding parts of triangles are congruent if the triangles themselves are congruent.
  • Congruent sides are defined as sides of triangles that have identical lengths.
  • ASA Postulate confirms that if two triangles have two pairs of corresponding angles and the included side congruent, the triangles are congruent.
  • SSS Postulate asserts that triangles are congruent if all three pairs of corresponding sides are congruent.
  • AAS Postulate states that if two angles and a non-included side in one triangle are congruent to those in another triangle, the triangles are congruent.
  • HL Postulate applies to right triangles, stating that if a hypotenuse and one leg of two right triangles are congruent, the triangles are congruent.
  • SAS Postulate indicates that if two sides and the included angle of a triangle are congruent to another triangle, the triangles are congruent.

Characteristics of Angles and Sides

  • Corresponding sides have the same relative position in geometric figures, crucial for determining congruence.
  • Corresponding angles share the same relative positions in geometric figures, similar in importance for congruence.
  • Third Angles Theorem states that if two angles in one triangle are congruent to two angles in another triangle, the third pair of angles must also be congruent.
  • The Isosceles Triangle Theorem suggests that if two sides of a triangle are congruent, the opposite angles to those sides are also congruent.
  • The converse of the Isosceles Triangle Theorem states that if two angles of a triangle are congruent, then the sides opposite those angles must also be congruent.

Types of Triangles

  • Congruent figures maintain the same shape and size, exhibiting congruence in all sides and angles.
  • An acute triangle contains three acute angles, while an obtuse triangle has one angle measuring over 90 degrees.
  • A right triangle contains exactly one 90-degree angle.
  • An equiangular triangle has all angles congruent, differing from a scalene triangle, which has no congruent sides.
  • An isosceles triangle features at least two congruent sides, and an equilateral triangle has all three sides congruent.

Triangle Geometry Theorems

  • The Triangle Sum Theorem establishes that the sum of the interior angles of a triangle is always 180 degrees.
  • The Exterior Angle Theorem states that the measure of an exterior angle is equal to the sum of the two remote interior angles.
  • Congruent triangles are defined by having the same shape and size, with all corresponding sides and angles being congruent.

Congruence Properties

  • CPCTC reinforces the idea that congruent triangles possess matching corresponding parts.
  • The Reflexive Property of Congruence indicates that a segment is always congruent to itself.
  • The Symmetric Property asserts that if one segment is congruent to another, then the converse is also true.
  • The Transitive Property allows for the conclusion that congruence can be transferred from one segment to another through a middle segment.

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Description

Test your understanding of the triangle congruence theorems and their properties. This quiz covers CPCTC, ASA, SSS, AAS, HL, and SAS postulates, evaluating your knowledge of triangle congruence criteria. Perfect for geometry students looking to reinforce their grasp on triangle relationships.

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