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4.6: Chapter 4 Review

Difficulty Level: At Grade Created by: CK-12
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Congruent Triangles and their corresponding parts

Definitions, Postulates, and Theorems

Triangle Sums

  • Interior Angles
  • Vertex
  • Triangle Sum Theorem
  • Exterior Angle
  • Exterior Angle Sum Theorem
  • Remote Interior Angles
  • Exterior Angle Theorem

Congruent Figures

  • Congruent Triangles
  • Congruence Statements
  • Third Angle Theorem
  • Reflexive Property of Congruence
  • Symmetric Property of Congruence
  • Transitive Property of Congruence

Triangle Congruence using SSS and SAS

  • Side-Side-Side (SSS) Triangle Congruence Postulate
  • Included Angle
  • Side-Angle-Side (SAS) Triangle Congruence Postulate
  • Distance Formula

Triangle Congruence using ASA, AAS, and HL

  • Angle-Side-Angle (ASA) Congruence Postulate
  • Angle-Angle-Side (AAS) Congruence Theorem
  • Hypotenuse
  • Legs (of a right triangle)
  • HL Congruence Theorem

Isosceles and Equilateral Triangles

  • Base
  • Base Angles
  • Vertex Angle
  • Legs (of an isosceles triangle)
  • Base Angles Theorem
  • Isosceles Triangle Theorem
  • Base Angles Theorem Converse
  • Isosceles Triangle Theorem Converse
  • Equilateral Triangles Theorem


For each pair of triangles, write what needs to be congruent in order for the triangles to be congruent. Then, write the congruence statement for the triangles.

  1. HL
  2. ASA
  3. AAS
  4. SSS
  5. SAS

Using the pictures below, determine which theorem, postulate or definition that supports each statement below.

  1. \begin{align*}m \angle 1 + m\angle 2 =180^\circ\end{align*}
  2. \begin{align*}\angle 5 \cong \angle 6\end{align*}
  3. \begin{align*}m \angle 1 + m\angle 4 + m\angle 3\end{align*}
  4. \begin{align*}m\angle 8 = 60^\circ\end{align*}
  5. \begin{align*}m \angle 5 + m\angle 6 + m\angle 7 =180^\circ\end{align*}
  6. \begin{align*}\angle 8 \cong \angle 9 \cong \angle 10\end{align*}
  7. If \begin{align*}m\angle 7 = 90^\circ\end{align*}, then \begin{align*}m\angle 5 = m\angle 6 = 45^\circ\end{align*}

Texas Instruments Resources

In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9689.

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