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GEOMETRY CHAPTER 4

CONGRUENT TRIANGLES

Unit 1 Apply Triangle Sum Properties

1. A triangle has vertices A(2, 3), B(6, 3) and C(2, 7). Graph the triangle and classify it by its sides and angles.

2. Find the value of x. Then classify the triangle by its angles.

3. Find the measure of the exterior angle shown.

4. Use the diagram to write a proof of the triangle sum theorem.

Prove: m(1 + m(2 + m(3 = 180(

Unit 2 Apply Congruence and Triangles

1. Explain what information is needed to prove that two triangles are congruent.

2. Identify all pairs of congruent corresponding parts. Then write another congruence statement for the triangles.

3. Use the diagram to complete each statement.

a. [pic]________

b. [pic]________

c. m(M = ________

d. m(P = ________

e. MT = ________

f. [pic]________

4. Complete a proof.

[pic]

Unit 3 Prove Triangles Congruent by SSS

1. Describe and correct the error in writing a triangle congruence statement.

2. Use the given coordinates to determine if [pic]

a. A(-2, -2), B(4, -2), C(4, 6), b. A(-5, 7), B(-5, 2), C(0, 2),

D(5, 7), E(5, 1), F(13, 1) D(0, 6), E(0, 1), F(4, 1)

3. Complete a proof.

[pic]

Unit 4 Prove Triangles Congruent by SAS and HL

1. Sketch a diagram and use it to explain the difference between proving triangles congruent using the SAS and SSS congruence postulates.

2. Decide whether enough information is given to prove that the triangles are congruent using the SAS congruence postulate. Explain your answer.

a. b.

3. State an example of every congruence that must be given to prove that the triangles are congruent by the given postulate.

a. SSS

b. SAS

c. HL

4. Complete a proof.

[pic]

Unit 5 Prove Triangles Congruent by ASA and AAS

1. If you know that a pair of triangles has two pairs of congruent corresponding angles, what other information do you need to show that the triangles are congruent?

2. Is it possible to prove that the triangles are congruent? If so, state the postulate or theorem that you would use and write a congruence statement.

a. b.

3. Describe the error.

4. State an example of every congruence that must be given to prove that the triangles are congruent by the given postulate.

a. AAS

b. ASA

Unit 6 Use Congruent Triangles

1. Tell which triangles you can show are congruent in order to prove the statement. Also tell which postulate or theorem you would use.

a. b.

2. Which of the triangles below are congruent? How do you know?

[pic]

3. Use the information given in the diagram to write a proof.

Unit 7 Use Isosceles and Equilateral Triangles

1. Are all equilateral triangles also isosceles triangles? Are all isosceles triangles also equilateral triangles? Explain.

2. Find the values of x and y.

a. b.

3. Make up a problem similar to #2 and solve your problem.

4. In triangle DEF, m(D = (4x + 2)(, m(E = (6x – 30)(, and m(F = 3x(. What type of triangle is DEF? Explain your reasoning.

5. The lengths of the sides of a triangle are 3t, 5t – 12, and t + 20. Find the values of t that make the triangle isosceles (there are three different answers).

Unit 8 Perform Congruence Transformations

1. Describe the translation in words: [pic]

2. Figure ABCD has vertices A(1, 2), B(4, -3), C(5, 5), and D(4, 7). Sketch ABCD and draw its image after the translation.

[pic]

3. Use coordinate notation to describe the translation.

a. 4 units to the left, 2 units down

b. 7 units to the right, 9 units up

4. Can a figure be its own image under a transformation? Explain your answer.

5. a. Find every capital letter of the alphabet that reflects onto itself

through a vertical line of reflection.

b. Find every capital letter of the alphabet that reflects onto itself

through a horizontal line of reflection.

c. Find every capital letter of the alphabet that reflects onto itself through a

rotation of 180(

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