1. M N O P R Q
1. How do you know that N R?
ANSWER
Third s Thm.
2. Write a triangle congruence statement.
ANSWER
∆MNO ∆PRQ

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

3. Proving triangles congruent.
Target
Proving triangles congruent.
GOAL:
4.4 Use side lengths to prove triangles congruent.

4. Vocabulary
SSS (Side-Side-Side) Congruence Postulate
If three sides of one triangle are congruent to
three sides of a second triangle,
then the two triangles are congruent.

5. EXAMPLE 1
Use the SSS Congruence Postulate
Write a paragraph proof.
GIVEN
KL NL, KM NM
PROVE
KLM NLM
Proof
It is given that
KL NL and KM NM
By the Reflexive Property,
LM LM.
So, by the SSS Congruence Postulate,
KLM NLM

6. GUIDED PRACTICE
for Example 1
Decide whether the congruence statement is true. Explain your reasoning.
DFG HJK
SOLUTION
If 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.
Therefore conditions of the hypothesis for SSS
have not been met and ABC cannot be congruent to
CAD because corresponding sides are not congruent.

8. 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.

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

10. 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.
Answer A (–1, 1), (–1, 5), (–4, 5)
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

11. 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.

12. 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

13. 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.

14. 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.

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