3.2 Three Ways to Prove a Triangle Congruent Kaylee Nelson Period: 8.
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3.2 Three Ways to Prove a Triangle Congruent Kaylee Nelson Period: 8
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Transcript of 3.2 Three Ways to Prove a Triangle Congruent Kaylee Nelson Period: 8.
3.2 Three Ways to Prove a Triangle Congruent
Kaylee NelsonPeriod: 8
Included Angles and Included Sides
An included angle is an angle made by two lines with a common vertex
An included side is a side that links two angles together
Three Ways to Prove Triangles Congruent
Angle-Side-Angle (ASA) Side-Side-Side (SSS) Side-Angle-Side (SAS)
The Angle – Side – Angle Postulate
The Angle – Side - Angle postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then these two triangles are congruent.
Sample Problem (ASA)
Since angle A is congruent to angle X, segment AB is
congruent to segment XY, and
angle B is congruent to angle Y, the triangles are congruent through
ASA.YB
XYAB
XA
The Side – Side – Side Postulate
The Side – Side - Side postulate states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.
Sample Problem (SSS)
Since segment ZX is congruent to segment CA,
segment XY is congruent to
segment AB, and segment YZ is congruent to
segment BC, the triangles are
congruent through SSS BCYZ
ABXY
CAZX
The Side – Angle – Side Postulate
The Side - Angle - Side postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
Sample Problem (SAS)
Since segment AC is congruent to
segment ZX, angle ACB is congruent to
angle XZY, and segment CB is congruent to
segment ZY, the triangles are
congruent through SAS ZYCB
XZYACB
ZXAC
Practice Problem One
ΔCBDΔABD:Conclusion
AC of midpt is B
CDAD :Given
Practice Problem Two
ΔPROΔKRM :Prove
PRMKRO
PRKR
63 :Given
Practice Problem Three
ΔAECΔADB :Conclusion
ADAE
ABAC :Given
Answer Key
Practice Problem One
ΔCBDΔABD 5.
BDBD 4.
CBAB 3.
AC of midpoint is B 2.
CDAD 1.
4) 3, (1, SSS 5.
property Reflexive 4.
segments congruent
two into seg the divides it
seg, a of midpt the is pt a If 3.
Given 2.
Given 1.
Practice Problem One
ΔCBDΔABD 5.
BDBD 4.
CBAB 3.
AC of midpoint is B 2.
CDAD 1.
4) 3, (1, SSS 5.
property Reflexive 4.
segments congruent
two into seg the divides it
seg, a of midpt the is pt a If 3.
Given 2.
Given 1.
Practice Problem Two
ΔPRMΔKRM 8.
PROKRM 7.
PRMKRO 6.
PRKR 5.
54 4.
6 to supp is 5 3.
4 to supp is 3 2.
63 1.
7) 5, (4, ASA 8.
property nSubtractio 7.
Given 6.
Given 5.
are s to supp s 4.
2 as Same 3.
supp are they diagram) from (assumed
straight a forms s two If 2.
Given 1.
Practice Problem Three
ΔAECΔADB 4.
AA 3.
ADAE 2.
ABAC 1.
3) 2, (1, ASA 4.
property Reflexive 3.
Given 2.
Given 1.
Works Cited
Morris, Vernon. "Proving Congruent Triangles." Math Warehouse. 28 May 2008<http://www.mathwarehouse.com/copyright.php>.
Page, John. Math Open Reference. 2007. 28 May 2008 <http://www.mathopenref.com/index.html>. Rhoad, Richard, George Milauskas, Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, Illinois:
McDougal, Littell & Company, 1991.
