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Unit 3: Congruent Triangles

Scale for Unit 3

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Through independent work beyond what was taught in class, I can (one example) create a

proof relating congruent triangles to the truss of a home.

3

I am able to:

Prove and utilize theorems about triangles.

Make a geometric construction of congruent triangles using a compass,

straightedge, or other mathematical tools.

Construct an equilateral triangle inscribed in a circle.

Use congruence and similarity criteria for triangles to solve problems and to prove

relationships in geometric figures.

2

I am able to:

Determine the meaning of symbols, key terms, and other geometry specific words

and phrases.

Utilize the Triangle Angle Sum Theorem.

Identify corresponding parts of congruent figures.

Recall how to construct a circle, segment, and angle.

Classify quadrilaterals

Understand two-column proofs.

Recall the distance formula.

Recall the properties of isosceles, equilateral, and right triangles.

1

I can correctly use the geometry vocabulary of angle, circle, segment, quadrilateral, two-

column proof, isosceles triangle, equilateral triangle, and right triangle.

Ranking:

Date

Level

Notes: (what you didn’t understand from the chapter and want to work on)

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Rank Yourself:

Level 4

Level 3

Level 2

Level 1

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BELLWORK:

Date: ___________________________

Date: ___________________________

Date: ___________________________

Date: ___________________________

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BELLWORK:

Date: ___________________________

Date: ___________________________

Date: ___________________________

Date: ___________________________

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Section 4-1 – Congruent Figures

EXAMPLES:

Label the congruent corresponding parts.

Are the following triangles congruent?

∆WYS ≅ ∆MKV. If m∠W = 62º and

m∠Y = 35º, what is m∠V?

Are the following triangles congruent?

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EXAMPLES: Can you conclude the two triangles are congruent? Justify your answer.

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EXAMPLES:

Prove that ∆ABC ≅ ∆CDA.

Statement Reason

Statement Reason

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Section 4-2 – Triangle Congruence By SSS and SAS

EXAMPLES: Would you use SSS, SAS, is there not enough information to prove the triangles are

congruent? Explain your answer.

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Statement Reason

Statement Reason

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Section 4-3 – Triangle Congruence By ASA and AAS

EXAMPLES: Complete the following Proofs.

Which two triangles are

congruent by the ASA

theorem?

Statement Reason

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Complete the following

proof.

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MIDUNIT REVIEW

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Section 4-4 – Using Corresponding Parts of Congruent Triangles

With ____, ____, ____, and ____, you know how to use three congruent

parts of two triangles to show that the triangles are congruent. Once

you know the triangles are congruent, you can make conclusions

about their corresponding parts because, by definition,

_________________________________________________________.

EXAMPLE: Complete the following proof.

Statement Reason

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SECTION REVIEW ACTIVITY:

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Section 4-5 – Isosceles and Equilateral Triangles

The congruent sides of isosceles

triangles are its ______. The third side is

the ______. The two congruent legs

form the ______ angle. The other two

angles are the ______ angles.

Label the parts of the diagram:

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EXAMPLES:

Find x and y:

Find x and y:

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Section 4-6 – Congruence in Right Triangles

In a right triangle, the side opposite of the

right angle is called the ______________. It is

the ____________ side of the triangle. The

other two sides are called _________.

Label the parts of the diagram:

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EXAMPLE: Complete the following proof.

Statement Reason

EXAMPLES: What values of x and y would make the triangles congruent by HL?

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Section 4-7 – Congruence in Overlapping Triangles

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UNIT 3 REVIEW:

Lesson 4-1

SAT GRE. Complete each congruence statement.

1. S ___. 2. GR ___.

3. E ___. 4. AT ___.

5. ERG _____. 6. EG ___.

7. REG ____. 8. R ___.

State whether the figures are congruent. Justify your answers.

9. ABF; EDC 10. TUV; UVW

11. XYZV; UTZV 12. ABD; EDB

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Lessons 4-2 and 4-3

Can you prove the two triangles congruent? If so, write the congruence statement and name the postulate you would use. If not, write not possible and tell what other information you would need. 13. 14.

15. 16.

17. Given: PX PY , ZP bisects XY . 18. Given: 1 2, 3 4, PD PC ,

Prove: PXZ PYZ P is the midpoint of AB .

Prove: ADP BCP

19. Given: 1 2, 3 4, AP DP 20. Given: , ,MP NS RS PQ MR NQ

Prove: ABP > DCP Prove: MQP NRS

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21. Given: 22. Given: OTS OES, EOS OST

Prove: MLN ONL Prove: TO ES

Lesson 4-4

23. Given: 1 2, 3 4, 24. Given: PO = QO, 1 2,

M is the midpoint of PR Prove: A B

Prove: PMQ RMQ

Lesson 4-5

Find the value of each variable.

25. 26. 27.

28. Given: 5 6, PX PY 29. Given: ,AP BP PC PD

Prove: PAB is isosceles. Prove: QCD is isosceles.

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Lessons 4-6 and 4-7

Name a pair of overlapping congruent triangles in each diagram. State whether the triangles are congruent by SSS, SAS, ASA, AAS, or HL.

30. 31.

32. 33.

34. Given: M is the midpoint of AB ,

, , 1 2MC AC MD BD Prove: ACM BDM

35. The longest leg of ABC, AC , measures 10 centimeters. BC measures 8 centimeters. You

measure two of the legs of XYZ and find that AC XZ and BC YZ . Can you conclude that two

triangles to be congruent by the HL Theorem? Explain why or why not.