4.6: Chapter 4 Review
Difficulty Level: At Grade
Created by: CK12
Definitions, Postulates, and Theorems
 Interior Angles
 The angles inside of a closed figure with straight sides.
 Vertex
 The point where the sides of a polygon meet.
 Triangle Sum Theorem

The interior angles of a triangle add up to \begin{align*}180^\circ\end{align*}
180∘ .
 Exterior Angle
 The angle formed by one side of a polygon and the extension of the adjacent side.
 Exterior Angle Sum Theorem

Each set of exterior angles of a polygon add up to \begin{align*}360^\circ\end{align*}
360∘ .
 Remote Interior Angles
 The two angles in a triangle that are not adjacent to the indicated exterior angle.
 Exterior Angle Theorem
 The sum of the remote interior angles is equal to the nonadjacent exterior angle.
 Congruent Triangles
 Two triangles are congruent if the three corresponding angles and sides are congruent.
 Third Angle Theorem
 If two angles in one triangle are congruent to two angles in another triangle, then the third pair of angles must also congruent.
 Reflexive Property of Congruence
 Any shape is congruent to itself.
 Symmetric Property of Congruence

If two shapes are congruent, the statement can be written with either shape on either side of the \begin{align*}\cong\end{align*}
≅ sign.
 Transitive Property of Congruence
 If two shapes are congruent and one of those is congruent to a third, the first and third shapes are also congruent.
 SideSideSide (SSS) Triangle Congruence Postulate
 If three sides in one triangle are congruent to three sides in another triangle, then the triangles are congruent.
 Included Angle
 When an angle is between two given sides of a triangle (or polygon).
 SideAngleSide (SAS) Triangle Congruence Postulate
 If two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.
 AngleSideAngle (ASA) Congruence Postulate
 If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent.
 AngleAngleSide (AAS or SAA) Congruence Theorem
 If two angles and a nonincluded side in one triangle are congruent to two corresponding angles and a nonincluded side in another triangle, then the triangles are congruent.
 HL Congruence Theorem
 If the hypotenuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.
 Base Angles Theorem
 The base angles of an isosceles triangle are congruent.
 Isosceles Triangle Theorem
 The angle bisector of the vertex angle in an isosceles triangle is also the perpendicular bisector to the base.
 Base Angles Theorem Converse
 If two angles in a triangle are congruent, then the opposite sides are also congruent.
 Isosceles Triangle Theorem Converse
 The perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle.
 Equilateral Triangles Theorem
 all sides in an equilateral triangle have exactly the same length.
Review
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.
 HL
 ASA
 AAS
 SSS
 SAS
Using the pictures below, determine which theorem, postulate or definition that supports each statement below.

\begin{align*}m \angle 1+m \angle 2=180^\circ\end{align*}
m∠1+m∠2=180∘ 
\begin{align*}\angle 5 \cong \angle 6\end{align*}
∠5≅∠6 
\begin{align*}m \angle 1=m \angle 4+ m \angle 3\end{align*}
m∠1=m∠4+m∠3 
\begin{align*}m \angle 8 = 60^\circ\end{align*}
m∠8=60∘ 
\begin{align*}m \angle 5+m \angle 6+m \angle 7=180^\circ\end{align*}
m∠5+m∠6+m∠7=180∘ 
\begin{align*}\angle 8 \cong \angle 9 \cong \angle 10\end{align*}
∠8≅∠9≅∠10  If \begin{align*}m \angle 7 = 90^\circ\end{align*}
m∠7=90∘ , then \begin{align*}m \angle 5 = m \angle 6 = 45^\circ\end{align*}m∠5=m∠6=45∘
Texas Instruments Resources
In the CK12 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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Tags:
angle theorems
CK.MAT.ENG.SE.1.GeometryBasic.4
CK.MAT.ENG.SE.2.Geometry.4
(11 more)
congruent figures
equilateral triangles
Exterior Angles Theorem
isosceles triangles
properties of congruence
Third Angle Theorem
triangle congruence
triangle congruence postulates
Triangle Sum Theorem
triangle sums
triangles
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Date Created:
Feb 22, 2012
Last Modified:
Feb 03, 2016
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