triangle based on inequality theorem S1+S2>S3
1. triangle based on inequality theorem S1+S2>S3
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2. Using the triangle in inequality theorem 3, what inequality will you write to check whether segments with lenghts S1,S2,S3 form a triangle if S1 < S2 < S3 ?
Answer:
[tex]S_{3}-S_{1}<S_{2}<S_{1}+S_{3}[/tex] , [tex]S_{3}>S_{1}[/tex]
Step-by-step explanation:
The triangle inequality states that:
Every side of a triangle is smaller than the sum of the other two.
This means that three inequalities must be true, like here for segments [tex]S_{1},S_{2} ,S_{3}[/tex] we have the following :
[tex]S_{1}<S_{2}+S_{3}[/tex]
[tex]S_{2}<S_{3}+S_{1}[/tex]
[tex]S_{3}<S_{1}+S_{2}[/tex]
The three statements above are equivalent to the next statement:
[tex]S_{3}-S_{1}<S_{2}<S_{1}+S_{3}[/tex]
where [tex]S_{3}-S_{1}>0[/tex] from the hypothesis that [tex]S_{1}<S_{3}[/tex]
Of course the same statement would be true if we switched [tex]S_{2}[/tex] in the middle for any other side of the triangle.
The triangle inequality is necessary for three segments to form a triangle.
In case that the equality [tex]S_{1}=S_{2}+S_{3}[/tex] is true, then there can be no triangle, but a segment which is the sum of the other two.
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Keywords: Triangle Inequality, Triangle, Segment, Inequality
3. Which of the following is NOT an inequality theorem for one triangle?A.Exterior Angle Inequality TheoremB.Hinge Theorem Triangle InequalityC.Triangle Inequality Theorem 1(Ss-->Aa)D.Theorem 3 (S1 + S2 > S3)
Answer:
D. theorem3(S1+S2>S3
Step-by-step explanation:
basta yu na yon
4. what theorem should marie use to justify her provedstatement in No.4?A.Converse of the hinge theoremB.Hinge theoremC.Triangle inequality theorem 1(Ss->Aa)D.Triangle inequality theorem 3(S1 +S2>S3)
Answer:
A.converse of th3 hinge theorem po ..paki follow po..thank u
5. 2. What triangle inequality theorem that states "the sum of the measures of any two sides of a triangle is greater than the measure of the third side"? a. Ss - Aa b. AaSs C. Sa - As d. S. + S2 S3
a. ss - aa b. ss c. ss d. sssaa
6. Which of the following is not an inequality theorem for one triangle? a. Triangle Inequality Theorem 1 (SsAa) b. Triangle Inequality Theorem 3 (S1 + S2 > S3) c. Exterior Angle Inequality Theorem d. Hinge Theorem Pa help ako mwhehe thank u!!
Answer:
A
7. Directions: Choose the letter of the correct answer. Shade the letter of your choice in youranswer sheet.1. If one side of a triangle is longer than the second side, then the measure of the angle oppositethe longer side is greater than the measure of the angle opposite the shorter side. Whatinequalities in triangle is being defined?a. Theorem 1:Side Angle Inequality Theorem (Ss - Aa)b. Theorem 2: Angle Side Inequality Theorem (Aa-Ss)C. Theorem 3:Triangle Inequality Theorem (S1+S? > S3)d. Exterior Angle Inequality Theorem2. If one angle of a triangle is larger than another angle, then the side opposite the larger angle islonger than the side opposite the smaller. What inequalities in triangle is being defined?a. Theorem 1:Side Angle Inequality Theorem (S$ - Aa)b. Theorem 2: Angle Side Inequality Theorem (Aa - Ss)c. Theorem 3:Triangle Inequality Theorem (S1+S2> S3)d. Exterior Angle Inequality Theorem3. In any triangle, the sum of the lengths of any two of its sides is greater than the length of itsthird side. What inequalities in triangle is being defined?a. Theorem 1: Side Angle Inequality Theorem (Ss - Aa)b. Theorem 2: Angle Side Inequality Theorem (Aa-Ss)c. Theorem 3: Triangle Inequality Theorem (S1+S2> Ss)d. Exterior Angle Inequality Theorem4. The measure of an exterior angle of a triangle is greater than the measure of either of the tworemote interior angles. What inequalities in triangle is being defined?a. Theorem 1: Side Angle Inequality Theorem (Ss - Aa)b. Theorem 2: Angle Side Inequality Theorem (Aa-Ss)C. Theorem 3: Triangle Inequality Theorem (S1 + S2 S3)d. Exterior Angle Inequality Theoremanalo of a triangle is greater
Answer:
1.A
2.D
3.C
4.A
5.B
pa brainlist na lang
8. 3. Which of the following would justify Ryan's conclusion in item no. 2? A. Converse of Hinge Theorem B. Hinge Theorem C. Triangle Inequality Theorem 1 (Ss-Aa) D. Triangle Inequality Theorem 3 (S1 + S2 > S3) 4. From the inequalities in the triangles shown, a conclusion can be reached using the converse of hinge theorem. Which of the following is the conclusion? A. MZIST>m_AST B. SI<SAC.SI~=STD.m<AST>m<ISTPLSS ANSWER CORRECTLY UNLESS REPORT
Answer:
3.c
4.d
Step-by-step explanation:
sana po makatulong ...ty po
9. 6. Does a triangle with side lengths of 15,12, and 9 exist? A. No C. Never B. Yes D. None of these are correct 7. What is a possible third side to a triangle with side lengths of 13 and 4? A 5 C. 9 B. 8 D. 12 8. From the inequalities in the triangles shown, Jarold concluded that LOHM > LEHM theorem on inequalities in triangle justifies his answer? 10 8 H. M 10 7 E A. Triangle Inequality Theorem 3 (S1 + S2> S3) C. Converse of Hinge Theorem B. Triangle Inequality Theorem 1 (Ss - Aa) D. Hinge Theorembk nmn po!!?
Answer:
6.B.yes
7.C.9
8.C.Converse of Hinge Theorem
Step-by-step explanation:
make me brainliest pls ty
10. Study the figure in no. 2 Notice that m/_5> m/_3 and m/_5>m/_ 1. which theorem justifies these observation?A, Triangle Inequality Theorem 1(Ss ->Aa) B, Triangle Inequality Theorem 2(Aa->SS) C, Triangle Inequality Theorem 3( SI+S2>S3) D, Exterior Angle Inequality theorom
Answer:
Exterior Angle Inequality TheoremThe outside angle of a triangle is greater than any non-adjacent inside angle
(click heart button or màrk as bràinliest if the answer helped you.)
11. What theorem justifies the three inequalities being written about the sides?a. Theorem 1 (Ss→Aa) b. Theorem 2 (Aa→Ss)c. Theorem 3 (S1+S2>S3)d. Converse of Hinge Theorem
Question: What theorem justifies the three inequalities being written about the sides?
Answer:
a. Theorem 1 (Ss→Aa)
b. Theorem 2 (Aa→Ss)
c. Theorem 3 (S1+S2>S3)d. Converse of Hinge Theorem
12. Directions: Choose the letter that corresponds to your answer. Write your answer on aseparate sheet of paper.1. Which of the following is not an inequality theorem for one triangle?A. Triangle Inequality Theorem 1 (Ss-Aa)B. Triangle Inequality Theorem 3 (S1 + S2 > S3)C. Exterior Angle Inequality TheoremD. Hinge Theorem2. Which of the angles is an exterior angle of ARPY?A. 22B. 23C. 24D. 274R3. Study the figure in no. 2. Notice that m25 > m23 and ni25 > m21. Which theoremjustifies these observations?A. Triangle Inequality Theorem 1 (Ss-Aa)B. Triangle Inequality Theorem 2 (Aa-Ss)C. Triangle Inequality Theorem 3 (S1 + S2 > S3)D. Exterior Angle Inequality Theorem4. Joshua forms triangles by bending a 16-inch wire. Which of the following sets of wirelengths successfully form a triangle?I. 4 in, 5 in, 6 inIII. 4 in, 5 in, 7 inII. 4 in, 4 in, 8 in IV. 3 in, 4 in, 9 inA. I, 11 B. I, III C. II, IV D. III, IV5. From the inequalities in the triangles shown below, Jaroid concluded thatmZOHM > MLEHM. Which theorem on inequalities in triangle justifies his answer?A. Triangle Inequality Theorem 3 (S1 + S2 > S3)B. Triangle Inequality Theorem 1 (Ss-Aa)C. Converse of Hinge TheoremD. Hinge Theorem810HM M10E6. Which side of the AMOV is the longest if m_M = 46°, M20 = 81° and MZV = 53°?a. MO B. MVC. OV D. cannot be determined
Answer:
1.D-Hinge Theorem
2.A
3.C
4.B
5.
6.D
13. 3. What formula will you use to find the perimeter of the figure below?O a. P= 4S O b. P=2(L + W) OC. P= S1+S2+S3 c. O d. P= S1+S2+S3+S4+S5
Answer:
A.
Step-by-step explanation:
P=4s
P=4(3 in)
P=12 in
14. Triangle inequality Theorem 1 ( Ss- Aa )if one side of a triangle is _______ than a second side. then the _______ opposite the first _______ is larger than the angle _______ the _______side.Triangle inequality Theorem 2 ( Aa- Ss)if one _______ of a triangle is ________ than a second angle, then the side opposite the ________ angle is ________ than the side opposite the second_________Triangle inequality Theorem 3 ( S1+ S2>S3)The _______of the _______ any sides of a triangle is _______ than the _______of the ________side.Exterior angle inequality Theorem ( EAIT)The measure of an_______ angle of a triangle is ______ than the _______ of either _________interior.pls paki sagot po kailangan ko n po
Answer:
Triangle inequality Theorem 1 ( Ss- Aa )
if one side of a triangle is longer than a second side. then the angle opposite the first side is larger than the angle opposite the second side.
Triangle inequality Theorem 2 ( Aa- Ss)
if one of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.
Triangle inequality Theorem 3 ( S1+ S2>S3
The sum of the lengths of any sides of a triangle is greater than the length of the third side
Exterior angle inequality Theorem ( EAIT)
The measure of an exterior angle of a triangle is greater than the measure of either remote interior.
#Hope it helps
15. 4. What triangle inequality theorem states that "If one side of a triangle is longer than a second side then the angle opposite the longer side is larger than the angle opposite the second side"? A. Exterior Angle Inequality Theorem B. Triangle Inequality Theorem 1 (Ss-Aa) C. Triangle Inequality Theorem 2 (Aa-Ss) D. Triangle Inequality Theorem 3 (S1 + S2 > S3)
Answer:
B. Triangle Inequality Theorem 1 (Ss→Aa)
Step-by-step explanation:
16. What I Have Learned Amaming You have reached this part of the module. To ensure your full understanding on the concepts related to illustrate theorems on triangle inequalities using Exterior Angle Inequality Theorem, Triangle Inequality Theorem, and Hinge Theorem), it's important that you are able define or state each statement below Triangle Inequality Theorem 1 (Ss - Aa) Triangle Inequality Theorem 2 (Aa - Ss) Triangle Inequality Theorem 3 (S1 + S2 > S3)
I hope it helps have a good day to you.
Pa follow plss.
17. the perimeter of a triangle is s1 + s2 + s3 true or false
Answer:
True
Step-by-step explanation:
The simplest polygon is the triangle, with three straight sides enclosing an area. To find the perimeter, P, of any triangle, you need to know the length each of the three sides, s:
P = s1 + s2 + s3
18. Direction: There are options given in the box below. These options are the theorems on triangle inequalities. On your Math Notebook, write the words and symbols that best describe in the statement. Triangle Inequality Theorem 2 (Aa → Ss) Triangle Inequality Theorem 3 (S1+S2 > S3) Theorem 1 (Ss - Aa) Exterior Angle Inequality Theorem Hinge Theorem or SAS Converse of Hinge Theorem or SSS Inequality Theorem Inequality Theorem 1. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.Pa answer naman po!
Step-by-step explanation:
the length of the side of a triangle are 10 and 4 what is the positive all of the three side
19. use the triangle inequality theorem 3 (s1 + s2 + s3) in determining whether the following numbers in cm can be side lengths.(yes or no) 1. 9,13,20 2. 3,4,8 3.4,25,30
1. No, because 9+13 is less than 20.
2. No, because 3+4 is less than 8.
3. Yes, because 4+25 is greater than 30 and the sum of any two sides is greater than the third side in a triangle.
any amount
09163917783
20. answer from the given choices. (2 points each)1. Which of the following is not an inequality theorem for one triangle?A Triangle Inequality Theorem 1 (Ss - Aa) C. Exterior Angle Inequality TheoremB. Triangle Inequality Theorem 3 (S1 + S2 > S3) D. Hinge Theorem
Answer:
answer is C
Explanation:
A, B, D all meet the requirements
C is not
21. Written Work #1 (15 points)Directions: Choose the letter that corresponds to your answer. Write your answer on the space provided.1. Which of the following is not an inequality theorem for one triangle?A. Triangle Inequality Theorem 1 (Ss-Aa)B. Triangle Inequality Theorem 3 (S1 + S2 > S3)C. Exterior Angle Inequality TheoremD. Hinge Theorem2. Which of the angles is an exterior angle of ARPY?A. 22 B. 23C. 24D. 273. Study the figure in no. 2. Notice that m_5 > m23 and m25 > m_1. Which theorem justifiesthese observations?A Triangle Inequality Theorem 1 (Ss-Aa)B. Triangle Inequality Theorem 2 (Aa-Ss)C. Triangle inequality Theorem 3 (S1 + S2 > S3)D. Exterior Angle Inequality Theorem4. Joshua forms triangles by bending a 16-inch wire. Which of the following sets of wire lengthssuccessfully form a triangle?I. 4 in, 5 in, 6 in III. 4 in, 5 in, 7 inII. 4 in, 4 in, 8 in IV. 3 in, 4 in, 9 in810A 1,11 B. I, III C. II, IV D. III, IV5. From the inequalities in the triangles shown below, Jarold concluded that mZOHM > MZEHM.Which theorem on inequalities in triangle justifies his answer?A. Triangle Inequality Theorem 3 (S1 + S2 > S3)B. Triangle Inequality Theorem 1 (Ss-Aa)C. Converse of Hinge Theorem10D. Hinge TheoremHME6. Which side of the AMOV is the longest if m2M = 46°, m20 = 81° and mzV = 53°?2. MOB. MV C. OV D. cannot be determined7. The measure of an exterior angle of a triangle is alwaysA greater than its adjacent interior angleB. less than its adjacent interior angleC. greater than either its remote interior anglesD. less than either its remote interior angles_8. In APEN, PE = 12 cm, EN = 9 cm, and PN = 11 cm. List the angles in order from smallest tolargest measureA m2P, MZE, M2N C. MZE, M2P, M2NB. mZP, M2N, MZE D. MZN, MZP, MZEА9309. List the sides of ASAN in order from longest to shortest measure.A. SA, AN, SN C. AN, SN, SAB. SA, SN, AN D. SN, SA, ANS300570N
Answer:
D. theorem 3(s1+s2>s3)
Step-by-step explanation:
num:1
22. Directions: Choose the letter that corresponds to your answer. Write your answer on the space provided.1. Which of the following is not an inequality theorem for one triangle?A. Triangle Inequality Theorem 1 (Ss-Aa)B. Triangle Inequality Theorem 3 (S1 + S2 > S3)C. Exterior Angle Inequality TheoremD. Hinge Theorem2. Which of the angles is an exterior angle of ARPY?A. 22B, 23C. 24D. 273. Study the figure in no. 2. Notice that m25 > m23 and m25 > m21. Which theorem justifiesthese observations?A. Triangle Inequality Theorem 1 (Ss-Aa)B. Triangle Inequality Theorem 2 (Aa-Ss)C. Triangle inequality Theorem 3 (S1 + S2 > S3)D. Exterior Angle Inequality Theorem4. Joshua forms triangles by bending a 16-inch wire. Which of the following sets of wire lengthssuccessfully form a triangle?1. 4 in, 5 in, 6 in III. 4 in, 5 in, 7 inII. 4 in, 4 in, 8 inIV. 3 in, 4 in, 9 inA. 1,11 B. I, III C. II, IV D. III, IV5. From the inequalities in thetriangles shown below, Jarold concluded that m2OHM > MZEHM.Which theorem on inequalities in triangle justifies his answer?A. Triangle Inequality Theorem 3 (S1 + S2 > S3)B. Triangle Inequality Theorem 1 (Ss-Aa)C. Converse of Hinge Theorem10D. Hinge Theorem106. Which side of the AMOV is the longest if m2M = 46°, M20 = 81° and m2V = 53°?a. MO B. MV C. OV D. cannot be determined7. The measure of an exterior angle of a triangle is alwaysA. greater than its adjacent interior angleB. less than its adjacent interior angleC. greater than either its remote interior anglesD. less than either its remote interior angles
BBCDC
Sana makatulong.
23. find the perimeter1. L=20cm W=10cm P=?2. S1=5cm S2=5cm S3=5cm P=? 3.S1=4cm S2=4cm S3=4cm S4=4cm P=? Patulong nman po kung anonh sagot dito
Step-by-step explanation:
1. P = 2 × (20 cm + 10 cm) = 60 cm
2. P = 5 cm + 5 cm + 5 cm = 15 cm
3. P = 4 cm + 4 cm + 4 cm + 4 cm = 16 cm
24. 5. From the inequalities in the triangles shown below, Jarold concluded that 0 m20HM > mzEHM. Which theorem on inequalities in triangle justifies his answer? A. Triangle Inequality Theorem 3 (S1 + S2 > S3) B. Triangle Inequality Theorem 1 (Ss-Aa) C. Converse of Hinge Theorem D. Hinge Theorem 8 6. Which. H 10 10 M
Step-by-step explanation:
Based on the given triangle, we can use the Hinge Theorem to justify Jarold's conclusion that Өm20HM > ӨzEHM. The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first triangle is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle. In this case, we have Өm20HM and ӨzEHM as the included angles, and the sides m20 and zEH are congruent, since they are opposite sides of the line. Therefore, we can conclude that Өm20HM > ӨzEHM, and hence, the third side of triangle m20HM is longer than the third side of triangle zEHM.
The answer is D. Hinge Theorem.
25. 6. List the sides of ALYK in order from least to greatest measure,A. LY, YK, LKC. LY, LK, KLB. YK, YZ, IKD. YR, LK, LY7. From the inequalities in the triangles shown, a conclusion can be reachedwong the converse or hinge theorem. Which of the following is the laststatement?A HM HMB. MOHM > MEHMD. m2 EHM> m2 OHM8. The Triangle Inequality Theorem states "The sum of the lengths of anytwo sides of a triangle is greater than the length of the third side".A. Exterior Angle Inequality TheoremB. Triangle Inequality Theorem 1 (Ss - Aa)C. Triangle Inequality Theorem 2 (Aa-> Ss)D. Triangle Inequality Theorem 3 (S1+S2>S3)9. What is the other term for SAS Inequality Theorem?A. Exterior Angle Inequality TheoremB. Triangle Inequality Theorem 1 (Ss - Aa)C. Triangle Inequality Theorem 2 (Aa-> Ss)D. Hinge Theorem10. What is the other term for SSS Inequality Theorem?A. Exterior Angle Inequality TheoremB. Triangle Inequality Theorem 1 (Ss - Aa)C. Triangle Inequality Theorem 2 (Aa -> Ss)D. Converse of Hinge Theorem
[tex]\large\purple{\boxed{ANSWER}}[/tex]
1. which of the following measurements can be a third side a triangle its if first two sides measure 185 m and 248 m?
THEREFORE: D. 433 m
2. In ∆kjT, kj= 7 in6 in jT in=4 in which of the following is set of the angle is correctly arranged from least to greatest?
THEREFORE: C. ∆T, ∆j, ∆K
3. the following statement below are false except
THEREFORE: A. The measure of an exterior angle of a triangle is lesser.
4. what theroem is being described from the statement below
THRERFORE: C. Hinge theorem
5. in ∆GUD. GU=DU and GD→G
THEREFORE: A. GU→GD-GU
6. List the sides of ALYK in order from least to greatest measure,
THEREFORE: A. LY, YK, LK
7. From the inequalities in the triangles shown, a conclusion can be reached
wong the converse or hinge theorem. Which of the following is the last
statement?
THEREFORE D. m2 EHM> m2 OHM
8. The Triangle Inequality Theorem states "The sum of the lengths of any
two sides of a triangle is greater than the length of the third side".
THEREFORE:A. Exterior Angle Inequality Theorem
9. What is the other term for SAS Inequality Theorem?
THEREFORE: B. Triangle Inequality Theorem 1 (Ss - Aa)
10. What is the other term for SSS Inequality Theorem?
THREFORE: C. Triangle Inequality Theorem 2 (Aa -> Ss)
#CARRYONLEARNING
26. 1. Which of the following is not an inequality theorem for one triangle? A Triangle Inequality Theorem 1 (Ss-Aa) B. Triangle Inequality Theorem 3 (S1 + S2 > S3) C. Exterior Angle Inequality Theorem D. Hinge Theorem 42. Which of the angles is an exterior angle of ARPY? A.<2 B.<3 C.<4 D.<73. Study the figure in no. 2. Notice that m_5 > m_3 and 725 > m2 1. Which theorem justifies these observations?A. Triangle Inequality Theorem 1 (S5-Aa) B. Triangle Inequality Theorem 2 (Aa+Ss) C. Triangle Inequality Theorem 3 (S1 + S2 > S3) D. Exterior Angle Inequality Theorem 4. Joshua forms triangles by bending a 16-inch wire. Which of the following sets of wire lengths successfully form a triangle?I.14 in, 5 in, 6 in Ill. 4 in, 5 in, 7 inII. 4 in, 4 in, 8 in IV. 3 in, 4 in, 9 inA.I,IIB.I,III C.II,IV D.III,IV 5. From the inequalities in the triangles shown below, Jarold concluded that MZOHM > MLEHM. Which theorem on inequalities in triangle justifies his answer? A. Triangle inequality Theorem 3 (S1 + S2 > S3) B. Triangle Inequality Theorem 1 (Ss-Aa) C. Converse of Hinge Theorem D. Hinge Theorem 6. Which side of the SMOV is the longest if nLM = 46°, nico 81° and mV = 530? A. MO B. MV C.OV D. cannot be determined7. The measure of an exterior angle of a triangle is always_______A.greater than its adjacent interior angleB.less than each adjacent interior angleC.greater than either its remote interior anglesD.less than its remote interior angles
Answer:
1.A2.A3.C4.B5.A6.B7.Bsana makatulong sainyo
27. Indicate the Triangle Inequality Theorem that is being illustrated in each item. Choose from the Theorems listed below and write the letter of the correct answer on the space provided before each number. A. Triangle Inequality Theorem 1 (Ss - Aa) B. Triangle Inequality Theorem 2 (Aa - Ss) C. Triangle Inequality Theorem 3 (S1 + S2 > Sa) D. Exterior Angle Inequality Theorem E. Hinge Theorem or SAS Inequality Theorem F. Converse of Hinge Theorem or SSS Inequality Theorem:
Answer:
kapag math talaga, mahirap.
basahin mo yung booklet
28. What is the perimeter of the triangle if the length of the sides of the triangle is defined by following functions: S1(x)= 2x+4 S2(x)= x2+5x+4 s3(x)= 6x-3
Answer:
x2+13x+5 just add the like terms
29. Use the Triangle Inequality Theorem S1 + S2 > S3 to tell whether a triangle cam have sides with the given lengths of 6, 8, 10. Show solution and give conclusions.________________________________________Thank you sa makakasagot! Btw, I really need the answer asap.
lengths. Explain
a. 4, 8, 10
4 + 8 > 10
12 > 10
True
Conclusion
4 + 10 >8
14 > 8
True
8 + 10 > 4
18 > 4
Truc
b. 7, 9, 18
7 + 9 > 18
16 > 18
False
7 + 18> 9
25 > 9
True
9 +18> 7
27 > 7
True
Conclusion:
30. What triangle inequality theorem states that “If one side of a triangle is longer than a second side, then the angle opposite the longer side is larger than the angle opposite the second side”? A. Exterior Angle Inequality Theorem B. Triangle Inequality Theorem 1 (Ss→Aa) C. Triangle Inequality Theorem 2 (Aa→Ss) D. Triangle Inequality Theorem 3 (S1 + S2 > S3)
Answer:
B. triangle inequality theorem 1 (Ss--> Aa
Step-by-step explanation:
Pa follow nlng po
