4.4 prove triangles congruent by sss you will use the side lengths to prove triangles are congruent....
TRANSCRIPT
4.4 Prove Triangles Congruent by SSS
• You will use the side lengths to prove triangles are congruent.
• Essential Question:
How can you use side lengths to prove triangles congruent?
You will see how toanswer this question by learningthe SSS Congruence Postulate.
predict
Warm-Up Exercises
ANSWER ∆MNO ∆PRQ
1. Write a congruence statement.
M
N O
P
R Q
Warm-Up Exercises
ANSWER Third s Thm.
2. How do you know that N R?
M
N O
P
R Q
Warm-Up Exercises
ANSWER 30
3. Find x.
(7x – 50)º(2x + 10)º
(3x)º
Warm-Up ExercisesEXAMPLE 1 Use the SSS Congruence Postulate
Write a flow chart proof.
GIVEN KL NL, KM NM
LM LN.
KLM NLM
PROVE KLM NLM
given
KL = NL
KM = NM
Reflexive Property
givenSSS
Warm-Up Exercises
Three sides of one triangle are congruent to three sides of second triangle then the two triangle are congruent.
GUIDED PRACTICE for Example 1
Decide whether the congruence statement is true. Explain your reasoning.
SOLUTION
Yes. The statement is true.
1. DFG HJK
Side DG HK, Side DF JH,and Side FG JK.
So by the SSS Congruence postulate, DFG HJK.
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Decide whether the congruence statement is true. Explain your reasoning.
SOLUTION
2. ACB CAD
BC ADGIVEN :
PROVE : ACB CAD
PROOF: It is given that BC AD By Reflexive propertyAC AC, But AB is not congruent CD.
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Therefore the given statement is false and ABC is not Congruent to CAD because corresponding sides are not congruent
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Decide whether the congruence statement is true. Explain your reasoning.
SOLUTION
QT TR , PQ SR, PT TSGIVEN :
PROVE : QPT RST
PROOF: It is given that QT TR, PQ SR, PT TS. So bySSS congruence postulate, QPT RST. Yes the statement is true.
QPT RST 3.
Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice
SOLUTION
By counting, PQ = 4 and QR = 3. Use the Distance Formula to find PR.
d = y2 – y1( )2x2 – x1( )2 +
Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice
= 25 5=
By the SSS Congruence Postulate, any triangle with side lengths 3, 4, and 5 will be congruent to PQR.
= + 1 – 4( )2– 1 (– 5( ) )2–PR
= 42 + (– 3 ) 2
= 42 + (– 3 2 5=(–4) – (–1)( )25 – 1)( 2 + = 25 )
The correct answer is A.ANSWER
The distance from (–1, 1) to (–1, 5) is 4. The distance from (–1, 5) to (–4, 5) is 3. The distance from (– 1, 1) to (–4, 5) is
Warm-Up ExercisesGUIDED PRACTICE for Example 2
JKL
has vertices J(–3, –2), K(0, –2), and L(–3, –8).
RST has vertices R(10, 0), S(10, – 3), and T(4, 0).
Graph the triangles in the same coordinate plane and show that they are congruent.
4.
KJ = SR = 3.ANSWER
JL = RT = 6.
LK = TS = 3 5.
Warm-Up ExercisesEXAMPLE 3 Solve a real-world problem
Structural Support
Explain why the bench with the diagonal support is stable, while the one without the support can collapse.
Warm-Up ExercisesEXAMPLE 3 Solve a real-world problem
The bench with a diagonal support forms triangles with fixed side lengths. By the SSS Congruence Postulate, these triangles cannot change shape, so the bench is stable. The bench without a diagonal support is not stable because there are many possible quadrilaterals with the given side lengths.
SOLUTION
Warm-Up ExercisesGUIDED PRACTICE for Example 3
Determine whether the figure is stable. Explain your reasoning.
SOLUTION
The figure is without a diagonal support is not stable Because there are many possible quadrilaterals with the given side lengths.
5.
Warm-Up ExercisesGUIDED PRACTICE for Example 3
Determine whether the figure is stable. Explain your reasoning.
SOLUTION
The diagonal support forms triangle with fixed side length by SSS congruence postulate, these triangles can not change shape. The figure is stable.
6.
Warm-Up ExercisesGUIDED PRACTICE for Example 3
Determine whether the figure is stable. Explain your reasoning.
SOLUTION
The diagonal support is not stable because the lower half of figure dies not have diagonal support.
7.
Warm-Up ExercisesDaily Homework Quiz
1. The vertices GHI and RST are G(–2, 5), H(2, 5), I(–2, 2), R(–9, 8), S(–5, 8), and T(–9, 5). Is GHI RST? Explain.
Yes. GH = RS = 4, HI = ST = 5, and IG = TR = 3. By the SSS post ., it follows that GHI RST.
ANSWER
Warm-Up ExercisesDaily Homework Quiz
Is ABC XYZ? Explain.2.
Yes. By the seg. Add. Post., AC XZ. Also , AB XY and BC YZ. So ABC XYZ by the SSS post.
ANSWER
• You will use the side lengths to prove triangles are congruent.
• Essential Question:
How can you use side lengths to prove triangles congruent?
• Two triangles with the same side lengths are congruent by the SSSCongruence Postulate.
Show that the sides can be matched so that all three pairs of corresponding sides are congruent.