Classify Triangles and Find Measures of Their Angles

Name: ______Block:______Chapter 4 – Congruent Triangles

Notes Learning Date Assignment Score What am I confident about? Target(s) Where do I need to spend more time? Am I weak on a prerequisite skill?

Learning Targets: Classify triangles and find measures of their angles. Identify congruent figures. Use theorems about isosceles and equilateral triangles. Use the side lengths to prove triangles are congruent. Use sides and angles to prove congruence. Use two more methods to prove congruence. Use congruent triangles to prove corresponding parts congruent.

1 Unit 4 Syllabus: Ch. 4 Congruent Triangles Block Date Topic Homework 3 B 11/11 4.1 Classifying Triangles Worksheet: 4.1 Identifying A 11/12 Triangles 4 B 11/13 4.2 Congruent Triangles Worksheet: 4.2 Congruent A 11/14 4.7 Isosceles and Equilateral Triangles Triangles and 4.7 Isosceles and Equilateral Triangles 5 B 11/17 4.1, 4.2, and 4.7 Quiz Khan Academy A 11/18 6 B 11/19 4.3 – 4.5 Congruent Triangle Proofs Day 1 Worksheet: 4.3-4.5 Proving A 11/20 Triangles Congruent 7 B 11/21 4.3 – 4.5 Congruent Triangle Proofs Day 2 Worksheet: 4.3-4.5 Review A 11/24 Open Note Quiz

8 B 11/25 4.6 CPCTC Proofs Worksheet: 4.6 CPCTC Thanksgiving Break 8 A 12/1 4.6 CPCTC Poofs Worksheet: 4.6 CPCTC 9 B 12/2 Review Day Ch 4 Review Worksheet A 12/3 10 B 12/4 Ch 4 Test Khan Academy A 12/5 ***Syllabus subject to change due to weather, pep rallies, illness, etc

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Name: ______Block: ______Date: ______HW: 4.1 Identifying Triangles

Match the triangle description with the most specific name. (1 point each)

2 ______

7. Can a right triangle also be obtuse? Explain why or why not. (2 points)

8. A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. A (3, 3), B (6, 9) , C (6, -3) (2 points)

3 For questions 9 and 10, find the value of x. Then classify the triangle by is angles (2 points) 9. 10.

x = x= Triangle: ______Triangle:

11. Find the measure of the exterior angle (2 points).

#12-17 Find the measure of the numbered angle. (1 point each) 12. m1= 13. m2 =

14. m3 = 15. m4 =

16. m5 = 17. m6 =

18. Find the values of x and y. (2 points)

HW: 4.2 Congruent Triangles and 4.7 Isosceles and Equilateral Triangles In the diagram, . Complete the statement.

4 1. 4. 2. 5.

7. Find the value of x. 8. Identify all pairs of congruent corresponding parts when

9. Suppose , , Complete the statement. mA = 90, and mF = 20. What is mH? Tell what theorem you used.

Find the unknown measure. 14. 15. 16.

AB = ______ML= ______m

Find the value of x and y.

17. 18. 19. 5 x = ______x = _____ x = ______

20. 21. 22.

x = _____ y = ______x = _____ y = ______x = _____ y = _____

Identify each figure as congruent or not congruent. For those that can be proven congruent, WRITE A CONGRUENCE STATEMENT.

23. 24. 25.

26. 27. 28

HW: 4.3-4.5 Proving Triangles Congruent

Select the method which will prove the triangles congruent, if possible.

6 ______

______

8. 9. 10.

ABC  ______by ______ABC  ______by ______ABC  ______by ______

11. 12. 13.

ABC  ______by ______ABC  ______by ______ABC  ______by ______

Name the included angle between the pairs of sides.

14. 15.

State the 3rd congruence that much be given to prove that . 7 17. Given: A X 18. Given: A X 19. Given: C Z B Y Method: AAS Theorem Method: ASA Theorem Method: AAS Theorem

Use the given coordinates to determine if  ABC DEF. (*Hint- distance formula or graph)

20. A ( 2, -2) B (5, 1) C (4, 8) 21. A ( 1, -1) B (-2, 2) C (-3, -4) D (7, 5) E (10, 8) F (9, 13) D (3, 2) E (6, -1) F (7, 5)

Tell whether you can use the given information to determine whether.

22. 23.

HW: 4.3-4.5 Review Directions: Complete all of the problems and show all work if necessary.

Determine which method you would use to prove the two triangles congruent. If none of the methods apply, write NONE.

1. ______2. ______3.______

8 4. ______5. ______6.______

Statements Reasons

1. BE  BC 1.______

2. A  D 2.______

3. ABE  CBD 3.______

4. ABE  DBC 4.______HW: 4.6 CPCTC

1) Complete the proof (1 point per line)

Statements Reasons 10 1. 1.

2. 2. 3. 3. 4. 4.

2) Complete the proof (2 point per line)

Given:

Prove:

Statements Reasons 1. Given

2. Two angles that form a linear pair are supplementary. 2. 3. Supplements of the same angle, or congruent angles, are 3. congruent. 4. 4. 5. 5.

3.) Complete the proof (2 point per line)

Statements Reasons 1.

1. 2. 2. 3. 3. Right angles are congruent. 11 4. 4. 5. 5.

4.) Complete the proof (2 points per line)

Statements Reasons 1. ; 1. Given

2. 2. 3. 3.

6. 6. 7. If two sides of a triangle are congruent, the angles 7. opposite them are congruent.

HW: Review Ch 4

Basic Triangle Information 1.) Given the diagram, identify the following triangles. a.) right scalene triangle ______b.) equiangular triangle ______c.) obtuse isosceles triangle. ______

2.) Given the diagram, identify the following terms. a.) In ABD, identify the vertex angle. ______b.) In ACD, identify the hypotenuse. ______c.) In ACD, identify the legs. ______, ______d.) In ABD, identify the legs. ______, ______

3.) Complete the sentence with always, sometimes, or never. 12 a.) An isosceles triangle is ______a right triangle. b.) An obtuse triangle is ______a right triangle. c.) An isosceles triangle is ______an equilateral triangle. d.) An obtuse triangle is ______an isosceles triangle.

Solve for the variables 4.) x = _____ 5.) x= ______

6.) x = ______7.) x = ______y = ______

8.) x = ______; y = ______9.) x = ______

10.) x = ______11.) x = ______

13 12.) Solve for the missing angles. m1 = _____ m2 = _____ m3 = _____

In each diagram, the given triangles are congruent. Solve for the variable. 13.) x = ______14.) x = ______

Solve for each variable. Show all work. 15.) x = ______16.) x = ______; y = ______

17.) x = ______; y = ______18.) x = ______

14 19.) What is the perimeter of the triangle? ______

Determine if the triangles are congruent. If so, state the postulate. 20.) ______21.) ______22.) ______

23.) ______24.) ______25.) ______

Complete the proof.

15 26.

Statements Reasons