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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