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Warm-Up Exercises
1. Write a congruence statement.
M
N O
P
R Q
Bell Work
2. How do you know that N R?
M
N O
P
R Q
Warm-Up Exercises
Side-Side-Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of a
second triangle, than the two triangles are congruent.
Note: Given three side lengths of a certain length, only one
triangle can be formed.
Notes
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Decide whether the congruence statement is true.
Explain your reasoning.
1. DFG HJK
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Decide whether the congruence statement is true.
Explain your reasoning.
2. ACB CAD
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Decide whether the congruence statement is true.
Explain your reasoning.
QPT RST 3.
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 1 Use the SSS Congruence Postulate
Write a proof.
GIVEN KL NL, KM NM
PROVE KLM NLM
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 ExercisesGUIDED PRACTICE for Example 3
Determine whether each figure is stable. Explain your
reasoning.
5. 6. 7.
Warm-Up Exercises
Side-Angle-Side (SAS) Congruent Postulate
If two sides and the included angle of one triangle are congruent
to two sides and the included angle of a second triangle, then
the two triangles are congruent.
Notes
Warm-Up ExercisesEXAMPLE 2 Use SAS and properties of shapes
In the diagram, QS and RP pass through
the center M of the circle. What can you
conclude about MRS and MPQ?
Warm-Up ExercisesEXAMPLE 4 Choose a postulate or theorem
Sign Making
You are making a canvas sign to hang on the triangular
wall over the door to the barn shown in the picture. You
think you can use two identical triangular sheets of
canvas. You know that RP QS and PQ PS . What
postulate or theorem can you use to conclude that
PQR PSR?
Warm-Up Exercises
Hypotenuse-Leg (HL) Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to
the hypotenuse and a leg of a second right triangle, then the two
triangles are congruent.
Notes
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
Use the diagram at the right.
3. Redraw ACB and DBC side by
side with corresponding parts in the
same position.
Warm-Up Exercises
Is there enough given information to prove the
triangles congruent? If there is, state the postulate or
theorem.
1. ABE, CBD
ANSWER SAS Post.
GUIDED PRACTICE
Warm-Up ExercisesEXAMPLE 1 Use the SAS Congruence Postulate
Write a proof.
GIVEN
PROVE
BC DA, BC AD
ABC CDA
Warm-Up Exercises
HomeworkHW: 4.4 (pg. 234-237) #5,6,18,28,29
4.5 (pg. 241-243) #10,14,22,26,34
For Tomorrow
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