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Section 2.5Exploring Congruent Triangles

Goal: Determine the minimum amount of information needed to prove that two triangles are congruent.

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Two shapes are congruent if all sides and angles in one, are equal to the sides and angles in the other.

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Name the corresponding sides and angles of the following triangles.

Are the triangles congruent?

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ΔABC ΔPQR

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= = =

Identify the congruent parts of the following triangles.Write the congruency statement, if possible.

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If I told you that the measure of X is 65°, and nothing else, is there onlyone triangle you could draw?

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If I told you that the length of YZ is 2.74 m, and nothing else, is there onlyone triangle you could draw?

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What if I gave you two pieces of information?

What if I gave you three pieces of information?

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There are minimum sets of angle and side measurements that, if known, allow you to conclude that two triangles are congruent.

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CONGRUENCE POSTULATES

(SSS) Side - Side - Side PostulateIf the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.SSS EXAMPLES

http://www.mathopenref.com/congruentsss.html

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(SAS) Side - Included Angle - Side PostulateIf two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. The included angle is the one that is between the two known sides.

SAS EXAMPLES

http://www.mathopenref.com/congruentsas.html

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(ASA) Angle - Included Side - Angle PostulateIf two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

http://www.mathopenref.com/congruentasa.html

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http://www.mathopenref.com/congruentaas.html

(AAS) Angle - Angle - Not Included Side PostulateIf two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent.

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http://www.mathopenref.com/congruentssa.html

Congruent Triangles - Why SSA doesn't work

Congruent Triangles - Why AAA doesn't work

http://www.mathopenref.com/congruentaaa.html

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Are the following triangles congruent? Why or why not?

If the triangles are congruent, state the congruence statement.

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Are the following triangles congruent? Why or why not?

If the triangles are congruent, state the congruence statement.

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Are the following triangles congruent? Why or why not?

If the triangles are congruent, state the congruence statement.

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If the triangles are congruent, state the congruence statement.

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2.5 Assignment: Nelson Foundations of Mathematics 11, Sec 2.5, pg, 106

Questions: 1 ‐ 4