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Lesson 4-4. Proving Congruence: SSS and SAS. Transparency 4-4. 5-Minute Check on Lesson 4-3. Refer to the figure. 1. Identify the congruent triangles. 2. Name the corresponding congruent angles for the congruent triangles. - PowerPoint PPT Presentation
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Lesson 4-4
Proving Congruence:SSS and SAS
5-Minute Check on Lesson 4-35-Minute Check on Lesson 4-35-Minute Check on Lesson 4-35-Minute Check on Lesson 4-3 Transparency 4-4
Refer to the figure.1. Identify the congruent triangles.
2. Name the corresponding congruentangles for the congruent triangles.
3. Name the corresponding congruent sides for the congruent triangles.
Refer to the figure.4. Find x.
5. Find mA.
6. Find mP if OPQ WXY and mW = 80, mX = 70, mY = 30.Standardized Test Practice:
A CB D30 70 80 100
5-Minute Check on Lesson 4-35-Minute Check on Lesson 4-35-Minute Check on Lesson 4-35-Minute Check on Lesson 4-3 Transparency 4-4
Refer to the figure.1. Identify the congruent triangles.
LMN RTS2. Name the corresponding congruent
angles for the congruent triangles.L R, N S, M T
3. Name the corresponding congruent sides for the congruent triangles.LM RT, LN RS, NM ST
Refer to the figure.4. Find x.3
5. Find mA. 63
6. Find mP if OPQ WXY and mW = 80, mX = 70, mY = 30.Standardized Test Practice:
A CB D30 70 80 100
Objectives
• Use the SSS Postulate to test for triangle congruence
• Use the SAS Postulate to test for triangle congruence
Vocabulary
• Included angle – the angle formed by two sides sharing a common end point (or vertex)
Postulates
• Side-Side-Side (SSS) Postulate: If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.
• Side-Angle-Side (SAS) Postulate: 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 triangles are congruent.
Side – Angle – Side (SAS)
Statements Reasons
Vertical Angles Theorem
SAS Postulate
ACB DCE (included angle)
AC = CD Given in problem
BC = CE Given
Given: AC = CD BC = CE
Prove: ABC = DEC
ABC DEC
Given: EI FH; FE HI; G is the midpoint of both EI and FH.
ENTOMOLOGY The wings of a moth form two triangles. Write a two-column proof to prove that FEG HIG if EI FH, FE HI, and G is the midpoint of both EI and FH.
Prove: FEG HIG
1. Given1.
Proof: ReasonsStatements
3. SSS3. FEG HIG
2. Midpoint Theorem2.
3. SSS
1. Given2. Reflexive
Proof: ReasonsStatements
1. 2.3. ABC GBC
Write a two-column proof to prove that ABC GBC if
Use the Distance Formula to show that the corresponding sides are congruent.
COORDINATE GEOMETRY Determine whether WDV MLP for D(–5, –1), V(–1, –2), W(–7, –4), L(1, –5), P(2, –1), and M(4, –7). Explain.
Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, WDV MLP by SSS.
Answer: By definition of congruent segments, all corresponding segments are congruent. Therefore, ABC DEF by SSS.
Determine whether ABC DEF for A(5, 5), B(0, 3), C(–4, 1), D(6, –3), E(1, –1), and F(5, 1). Explain.
Write a flow proof.
Given:
Prove: QRT STR
Answer:
Write a flow proof.
Given:
Prove: ABC ADC
Proof:
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
Answer: SAS
Two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle. The triangles are congruent by SAS.
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
Answer: SSS
Each pair of corresponding sides are congruent. Two are given and the third is congruent by Reflexive Property. So the triangles are congruent by SSS.
Answer: SAS
Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove that they are congruent, write not possible.
a.
Answer: not possible
b.
Summary & Homework
• Summary:– If all of the corresponding sides of two triangles
are congruent, then the triangles are congruent (SSS).
– If two corresponding sides of two triangles and the included angle are congruent, then the triangles are congruent (SAS).
• Homework: – Pg 266-8: 4, 16-19, 24, 25
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