1. 4.4 Prove Triangles Congruent by SSS
predict
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 to
answer this question by learning
the SSS Congruence Postulate.

2. 1. Write a congruence statement.P R Q
ANSWER
∆MNO ∆PRQ

3. 2. How do you know that N R? M N O P R Q
ANSWER
Third s Thm.

4. 3. Find x.
(7x – 50)º
(2x + 10)º
(3x)º
ANSWER 30

5. EXAMPLE 1
Use the SSS Congruence Postulate
Write a flow chart proof.
GIVEN
KL NL, KM NM
PROVE
KLM NLM
KL = NL
KLM NLM
given
KM = NM
SSS
given
LM LN.
Reflexive Property

6. GUIDED PRACTICE
for Example 1
Decide whether the congruence statement is true. Explain your reasoning.
DFG HJK
SOLUTION
Three sides of one triangle are congruent to three sides of second triangle then the two triangle are congruent.
Side DG HK, Side DF JH,and Side FG JK.
So by the SSS Congruence postulate, DFG HJK.
Yes. The statement is true.

7. GUIDED PRACTICE
for Example 1
Decide whether the congruence statement is true. Explain your reasoning. 2.
ACB CAD
SOLUTION
BC AD
GIVEN :
PROVE :
ACB CAD
PROOF:
It is given that BC AD By Reflexive property
AC AC, But AB is not congruent CD.

8. GUIDED PRACTICE
for Example 1
Therefore the given statement is false and ABC is not
Congruent to CAD because corresponding sides
are not congruent

9. GUIDED PRACTICE
for Example 1
Decide whether the congruence statement is true. Explain your reasoning.
QPT RST 3.
SOLUTION
QT TR , PQ SR, PT TS
GIVEN :
PROVE :
QPT RST
PROOF:
It is given that QT TR, PQ SR, PT TS. So by
SSS congruence postulate, QPT RST. Yes the statement is true.

10. Standardized Test Practice
EXAMPLE 2
Standardized Test Practice
SOLUTION
By counting, PQ = 4 and QR = 3. Use the Distance Formula to find PR. d = y 2 – 1 ( ) x +

11. Standardized Test Practice
EXAMPLE 2
Standardized Test Practice = + 1 – 4 ( ) 2
– 1
(– 5
) ) PR = 4 2 +
(– 3 ) = 25 5 =
By the SSS Congruence Postulate, any triangle with side lengths 3, 4, and 5 will be congruent to
PQR.
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 = 4 2 +
(– 3 5
(–4) – (–1) ( )
5 – 1) 25
The correct answer is A.
ANSWER

12. GUIDED PRACTICE
for Example 2 4.
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.
JKL
KJ = SR = 3.
ANSWER
JL = RT = 6.
LK = TS =

13. EXAMPLE 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.

14. EXAMPLE 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

15. GUIDED 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.

16. GUIDED 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.

17. GUIDED PRACTICE
for Example 3
Determine whether the figure is stable. Explain your reasoning. 7.
SOLUTION
The diagonal support is not stable because the lower half of figure dies not have diagonal support.

18. Daily 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

19. Daily 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

20. 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 SSS
Congruence Postulate.
Show that the sides can be matched so that all three pairs of corresponding sides are congruent.