Five-Minute Check (over Lesson 4–3)
Then/Now
New Vocabulary
Postulate 4.1: Side-Side-Side (SSS) Congruence
Example 1: Use SSS to Prove Triangles Congruent
Example 2: Standard Test Example
Postulate 4.2: Side-Angle-Side (SAS) Congruence
Example 3: Real-World Example: Use SAS to Prove Triangles are Congruent
Example 4: Use SAS or SSS in Proofs
Over Lesson 4–3
A. A
B. B
C. C
D. D A B C D
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A. ΔLMN ΔRTS
B. ΔLMN ΔSTR
C. ΔLMN ΔRST
D. ΔLMN ΔTRS
Write a congruence statement for the triangles.
Over Lesson 4–3
A. A
B. B
C. C
D. D A B C D
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A. L R, N T, M S
B. L R, M S, N T
C. L T, M R, N S
D. L R, N S, M T
Name the corresponding congruent angles for the congruent triangles.
Over Lesson 4–3
A. A
B. B
C. C
D. D A B C D
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Name the corresponding congruent sides for the congruent triangles.
A. LM RT, LN RS, NM ST
B. LM RT, LN LR, LM LS
C. LM ST, LN RT, NM RS
D. LM LN, RT RS, MN ST
______ ___ ______ ___
___ ___ ___ ___ ___ ___
___ ______ ___ ___ ___
___ ___ ___ ___ ___ ___
Over Lesson 4–3
A. A
B. B
C. C
D. D A B C D
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A. 1
B. 2
C. 3
D. 4
Refer to the figure. Find x.
Over Lesson 4–3
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. 30
B. 39
C. 59
D. 63
Refer to the figure.Find m A.
Over Lesson 4–3
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Given that ΔABC ΔDEF, which of the following statements is true?
A. A E
B. C D
C. AB DE
D. BC FD___ ___
___ ___
You proved triangles congruent using the definition of congruence. (Lesson 4–3)
• Use the SSS Postulate to test for triangle congruence.
• Use the SAS Postulate to test for triangle congruence.
• included angle
Use SSS to Prove Triangles Congruent
Write a 2-column proof.
Prove: ΔQUD ΔADUGiven: QU AD, QD AU
___ ___ ___ ___
A. A
B. B
C. C
D. D A B C D
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Write a two-column proof.Given: AC AB
D is the midpoint of BC.Prove: ΔADC ΔADB
___ ___
EXTENDED RESPONSE Triangle DVW has vertices D(–5, –1), V(–1, –2), and W(–7, –4). Triangle LPM has vertices L(1, –5), P(2, –1), and M(4, –7).a. Graph both triangles on the same coordinate
plane.b. Use your graph to make a conjecture as to
whether the triangles are congruent. Explain your
reasoning.c. Write a logical argument that uses coordinate
geometry to support the conjecture you made in
part b.
b. From the graph, it appears that the triangles have the same shapes, so we conjecture that they are congruent.
c. Use the Distance Formula to show all corresponding sides have the same measure.
Answer: WD = ML, DV = LP, and VW = PM. By definition of congruent segments, all corresponding segments are congruent. Therefore, ΔWDV ΔMLP by SSS.
Use SAS to Prove Triangles are Congruent
ENTOMOLOGY The wings of one type of moth form two triangles. Write a two-column proof to prove that ΔFEG ΔHIG if EI HF, and G is the midpoint of both EI and HF.
Use SAS to Prove Triangles are Congruent
3. 3. FGE HGI
2. 2.
Prove: ΔFEG ΔHIG
4. 4. ΔFEG ΔHIG
Given: EI HF; G is the midpoint of both EI and HF.
1. 1. EI HF; G is the midpoint ofEI; G is the midpoint of HF.
Proof:ReasonsStatements
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
3. 3. ΔABG ΔCGB
2. 2.
1.
ReasonsProof:Statements
1.
Use SAS or SSS in Proofs
Write a 2-column proof.
Prove: Q S
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Write a 2-column proof.