Download - Congruent Triangles
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Congruent Triangles
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Helpful websites
• http://www.regentsprep.org/Regents/mathb/1c/preprooftriangles.htm
• http://www.mathwarehouse.com/geometry/congruent_triangles/
• http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Congruent-Triangles.topicArticleId-18851,articleId-18788.html
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4-1 Congruent Figures
Objective: To recognize congruent figures and their
corresponding parts
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Vocabulary/ Key Concept
• Congruent polygons- two polygons are
congruent if their corresponding sides and angles are congruent
• If two angles in a triangle are congruent to two angles in another triangle, then the third angles are congruent.
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Each pair of polygons are congruent. Find the measure of each numbered angle
• M1 = 110• m 2 = 120
• M3 = 90• m 4 = 135
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WXYZ JKLM. List 4 pairs of congruent sides and angles.
• WX JK• XY KL• YZ LM• ZW MJ
• W J• K X• Y L• Z M
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Determine if the polygons are congruent. Explain.
1.G I , GJH IJH,2.GHJ IHJ 3. JI GJ, GH IH,4. JH JH
GHJ and IHJ are congruent because all corresponding angle and sides are congruent
1.Given –congruent markings2.If two angles in a triangle are congruent
to two angles in another triangle, then the third angles are congruent.
3.Given-congruent markings4.Reflexive
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Determine if the polygons are congruent. Explain.
1.Q T2.QSR TSV3.R VNo, the triangles do no
have corresponding sides that are congruent
1.Given – congruent measures2.Vertical angles3. If two angles in a triangle are
congruent to two angles in another triangle, then the third angles are congruent.
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PROOF
Statement1. LM QP LN QN MN PN L Q2. LNM QNP 3. P M4. LMN QPN
Reasons1. GIVEN2. VEERITCAL ANGLES3. If two angles in a
triangle are congruent to two angles in another triangle, then the third angles are congruent
4. 4. Def. of congruent polygons
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4-2 Congruent Triangles by SSS and SAS
Objective:To prove two triangles are congruent using SSS
and SAS Postulates
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Key Concepts
• SSS – Side-side-side corresponding congruence.
• SAS – Side-Angle-Side corresponding Congruence.
ANGLE MUST BE IN BETWEEN THE TWO SIDE
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Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.
ABD CBD by SAS
AB CB --CONGRUENCE MARKING BD BD -- REFLEXIVEABD CBD –CONGRUENCE MARKING
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Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.
What do you know?NP = QP -- CONGRUENT MARKSNR = QR -- CONGRUENT MARKSRP = RP -- REFLEXIVE PROPERTY OF
PRN PRQ by SSS
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Determine if you can use SSS or SAS to prove two triangles are congruent. Write the congruence statement.
EM PQ EN PR CONGRUENCE MARKINGN R
Not possible
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Proof
Statements 1. AB DC, BAC DCA2. AC CA3. ABC CDA
Reasons1. Given2. Reflexive property of 3. SAS
A B
D C
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Try: Write a proof.
Statement1. EF GF, HF DF2. DFE HFG3. DFE HFG
Reasons1. Given2. Vertical angles3. SAS
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4-3 Congruent Triangles by AAS and ASA
Objective:To prove two triangles are congruent using AAS
and ASA Postulates
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Key Concepts
• ASA – Two angles and an included side.
• AAS – Two angles and a non-included side.
SIDE IS IN BETWEEN THE ANGLES
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Determine if you can use ASA or AAS to prove two triangles are congruent. Write the congruence statement.
TUV VST by ASA
not possible
BCEDCF by AAS
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Write a Proof
Statement 1. KL ML, K M2. JLK PLM3. JKL PML
Reasons 1. Given2. Vertical angles3. ASA
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What did you learn today?
• What are some simple steps to writing proofs?
• What are the four ways to prove triangles are congruent?