Isosceles Triangle Theorem and Congruence
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Questions and Answers

What are the angles opposite equal sides in an isosceles triangle called?

Base angles

What is the angle formed by the two equal sides in an isosceles triangle called?

Vertex angle

What is the name for one of the equal sides of an isosceles triangle?

Leg

The Isosceles Triangle Theorem states that if two sides of a triangle are equal, then the opposite angles are also equal.

<p>True (A)</p> Signup and view all the answers

What is the purpose of an auxiliary line in a proof?

<p>To aid in a proof</p> Signup and view all the answers

What does CPCTC stand for?

<p>Corresponding Parts of Congruent Triangles are Congruent (C)</p> Signup and view all the answers

An equilateral triangle is also equiangular according to Corollary 1 of the Isosceles Triangle Theorem.

<p>True (A)</p> Signup and view all the answers

Corollary 2 of the Isosceles Triangle Theorem states that if two angles of a triangle are equal, then the opposite sides are also equal.

<p>True (A)</p> Signup and view all the answers

What is the special relationship between the angle bisector and the base in an isosceles triangle, as stated in Corollary 3?

<p>The angle bisector is perpendicular to the base at its midpoint.</p> Signup and view all the answers

The Converse of the Isosceles Triangle Theorem states that if two angles of a triangle are equal, then the opposite sides are also equal.

<p>True (A)</p> Signup and view all the answers

What does the AAS Theorem state about triangle congruence?

<p>Two angles and a non-included side determine congruence.</p> Signup and view all the answers

According to the HL Theorem, what determines congruence in right triangles?

<p>The hypotenuse and leg</p> Signup and view all the answers

What is a median of a triangle?

<p>A segment from a vertex to the midpoint of the opposite side.</p> Signup and view all the answers

What is an altitude of a triangle?

<p>A perpendicular segment from a vertex to the opposite side.</p> Signup and view all the answers

What is a perpendicular bisector of a segment?

<p>A line that is perpendicular to a segment at its midpoint.</p> Signup and view all the answers

According to the definition of triangle congruence, when are triangles considered congruent?

<p>Triangles are congruent if their corresponding parts are equal.</p> Signup and view all the answers

What is an angle bisector?

<p>A ray that divides an angle into two equal angles.</p> Signup and view all the answers

What are interior angles of a triangle, and what is their sum?

<p>Interior angles are the angles inside a triangle, and their sum is always $180$ degrees.</p> Signup and view all the answers

What are congruent triangles?

<p>Triangles that are identical in shape and size.</p> Signup and view all the answers

What is the SAS Congruence criterion?

<p>Two sides and the included angle are equal.</p> Signup and view all the answers

What is a triangle proof?

<p>A logical argument demonstrating triangle properties.</p> Signup and view all the answers

Flashcards

Base Angles

Angles opposite equal sides in an isosceles triangle.

Vertex Angle

Angle formed by the two equal sides.

Leg

One of the equal sides of an isosceles triangle.

Isosceles Triangle Theorem

If two sides are equal, opposite angles are equal.

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Auxiliary Line

A line drawn to aid in a proof.

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CPCTC

Corresponding Parts of Congruent Triangles are Congruent.

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Corollary 1

An equilateral triangle is also equiangular.

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Corollary 2

If two angles are equal, opposite sides are equal.

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Corollary 3

Angle bisector is perpendicular to base at midpoint.

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Converse of Isosceles Triangle Theorem

If two angles are equal, opposite sides are equal.

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AAS Theorem

Two angles and a non-included side determine congruence.

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ASA Theorem

Two angles and the included side determine congruence.

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HL Theorem

Hypotenuse and leg of right triangles determine congruence.

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Median of a Triangle

Segment from a vertex to the midpoint of opposite side.

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Altitude

Perpendicular segment from a vertex to opposite side.

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Perpendicular Bisector

Line that is perpendicular to a segment at its midpoint.

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Triangle Congruence

Triangles are congruent if their corresponding parts are equal.

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Angle Bisector

Ray that divides an angle into two equal angles.

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Interior Angles

Angles inside a triangle that sum to 180 degrees.

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Congruent Triangles

Triangles that are identical in shape and size.

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SAS Congruence

Two sides and the included angle are equal.

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SSS Congruence

All three sides of triangles are equal.

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Triangle Proof

Logical argument demonstrating triangle properties.

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Equilateral Triangle

A triangle with all sides equal.

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Equiangular Triangle

A triangle with all angles equal.

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Side of a Triangle

A line segment connecting two vertices of a triangle.

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Vertex of a Triangle

A point where two sides of a triangle meet.

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Interior Angles of a triangle

Angles inside a triangle that sum to 180 degrees.

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Exterior Angle of a triangle

Angles outside of a triangle that are created by extending a side.

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Study Notes

Isosceles Triangle Theorem

  • Base Angles: Angles opposite equal sides in an isosceles triangle.
  • Vertex Angle: Angle formed by the two equal sides of an isosceles triangle.
  • Leg: One of the equal sides of an isosceles triangle.
  • Isosceles Triangle Theorem: If two sides of a triangle are equal, the angles opposite those sides are equal.
  • Auxiliary Line: A line drawn to aid in a proof.

Triangle Congruence & Theorems

  • CPCTC: Corresponding Parts of Congruent Triangles are Congruent.
  • Corollary 1: An equilateral triangle is also equiangular.
  • Corollary 2: If two angles of a triangle are equal, the sides opposite those angles are also equal.
  • Corollary 3: The angle bisector of an isosceles triangle is perpendicular to the base at its midpoint.
  • Converse of Isosceles Triangle Theorem: If two angles of a triangle are equal, the sides opposite those angles are also equal.

Triangle Congruence Postulates

  • AAS Theorem: Two angles and a non-included side determine congruence.
  • ASA Theorem: Two angles and the included side determine congruence.
  • HL Theorem: Hypotenuse and leg of right triangles determine congruence.
  • SAS Congruence: Two sides and the included angle determine congruence.
  • SSS Congruence: All three sides of two triangles are equal.

Triangle Parts & Properties

  • Median: A segment from a vertex to the midpoint of the opposite side.
  • Altitude: A perpendicular segment from a vertex to the opposite side.
  • Perpendicular Bisector: A line perpendicular to a segment at its midpoint.
  • Angle Bisector: A ray that divides an angle into two equal angles.
  • Interior Angles: Angles inside a triangle that sum to 180 degrees.
  • Congruent Triangles: Triangles that are identical in shape and size.
  • Triangle Proof: Logical argument demonstrating triangle properties.

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Description

Test your understanding of the Isosceles Triangle Theorem and related triangle congruence concepts. This quiz covers key definitions and theorems, including vertex angles, base angles, and various triangle congruence postulates. Determine your mastery of this essential geometry topic.

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