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4.4 Proving Triangles Congruent- SSS, SAS
Then: You proved triangles congruent using the definition of congruence. Now: 1. Use the SSS Postulate to test for triangle congruence. 2. Use the SAS Postulate to test for triangle congruence.
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Review: Write a congruence statement for the triangles: How do you know that the triangles are congruent?
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Postulate 4.1: Side-Side-Side (SSS) Congruence
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. If Side AB ______, Side BC ______, and Side AC ______. Then ABC ________
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Example 1: Use SSS to prove triangles congruent
a. Given: FJ HJ, G is the midpoint of FH. Prove: FGJ HGJ 1. It is given that FJ ________. 2. Point G is the midpoint of FH, so _____________. 3. By the Reflexive Property, __________________. 4. By the ___________________________, FGJ HGJ.
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Example 1: Use SSS to prove triangles congruent
b. Given: RS UT, RT US Prove: RST UTS Statements Reasons 1. RS UT, RT US 1. _______________ 2. ST TS _______________ 3. RST UTS _______________
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Example 2: SSS on the coordinate plane
DFG has vertices D(-2,4), F(4,4), and G(-2,2). LMN has vertices L(-3,-3), M(-3,3) and N(-1,-3). Graph the triangles in the same coordinate plane and show that they are congruent. If sides are vertical or horizontal, count spaces. If not, use distance formula: (x2 – x1)2 + (y2 – y1)2
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Example 2 continued DF = DG = GF = ML = LN = MN = ____________ ______________ by _______________________________
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Postulate 4.2: Side-Angle-Side (SAS) Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent. If Side RT ______, Angle R ______, and Side RS ______, Then RST ________
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Example 3: Use SAS to prove triangles congruent
a. Given: V is the midpoint of YZ V is the midpoint of WX. Prove: XVZ WVY 1. Since V is the midpoint of YZ and WX, __________ _______________________________________. 2. Since YVW and XVZ are __________________ _______________________________________ 3. Therefore, by _________________, _____ ____
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Example 3: Use SAS to prove triangles congruent
b. Given: AB = CD, AB CD Prove: DBA ACD Statements Reasons 1. AB = CD, AB CD 1. _________________ 2. DAB ADC 2. _________________ 3. AD = AD 3. _________________ 4. DBA ACD 4. _________________
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Example 4: Use SSS or SAS For each diagram, determine which pairs of triangles can be proved congruent. a. b. c. d.
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4.4 Assignment p #5, 6,12-15 and 24 are proofs on handout. #8 and #10- graph and use distance formula for all sides that are not vertical or horizontal. #16-19, 27, 28, and 30 on own paper or on graph paper.
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