congruent triangles
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Congruent Triangles. 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. - PowerPoint PPT PresentationTRANSCRIPT
Congruent Triangles
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
4-1 Congruent Figures
Objective: To recognize congruent figures and their
corresponding parts
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.
Each pair of polygons are congruent. Find the measure of each numbered angle
• M1 = 110• m 2 = 120
• M3 = 90• m 4 = 135
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
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
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.
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
4-2 Congruent Triangles by SSS and SAS
Objective:To prove two triangles are congruent using SSS
and SAS Postulates
Key Concepts
• SSS – Side-side-side corresponding congruence.
• SAS – Side-Angle-Side corresponding Congruence.
ANGLE MUST BE IN BETWEEN THE TWO SIDE
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
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
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
Proof
Statements 1. AB DC, BAC DCA2. AC CA3. ABC CDA
Reasons1. Given2. Reflexive property of 3. SAS
A B
D C
Try: Write a proof.
Statement1. EF GF, HF DF2. DFE HFG3. DFE HFG
Reasons1. Given2. Vertical angles3. SAS
4-3 Congruent Triangles by AAS and ASA
Objective:To prove two triangles are congruent using AAS
and ASA Postulates
Key Concepts
• ASA – Two angles and an included side.
• AAS – Two angles and a non-included side.
SIDE IS IN BETWEEN THE ANGLES
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
Write a Proof
Statement 1. KL ML, K M2. JLK PLM3. JKL PML
Reasons 1. Given2. Vertical angles3. ASA
What did you learn today?
• What are some simple steps to writing proofs?
• What are the four ways to prove triangles are congruent?