Unit #4: Triangle Congruence

Congruent Triangles

SSS

SAS

AAS

HL

ASA

Congruence Statement

Reason

Corresponding Parts

Reflexive Property

I. Name the congruent triangles.

1.2.

3. 4.

II. Name the congruent triangle and the congruent parts..

7.

Use the congruency statement to fill in the corresponding congruent parts.

8.

9. . Find x.10. Find y.

Third Angles Theorem (add to Theorems, Postulates and Definitions Card) –

Triangle Congruence Worksheet #1

For each pair of triangles, tell which postulates, if any, make the triangles congruent.

12. ABC EFD______13. ABC CDA ______

14. ABC EFD______15. ADC BDC______

21. MAD MBC______ABE CDE______

23. ACB ADB______23. ______

23. ______

Triangle Congruence Worksheet #2

I. For each pair of triangles, tell which postulate, if any, can be used to prove the triangles congruent.

1. AEB DEC______2. CDE ABF ______

3. DEABEC______4. AGE CDF ______

5. RTS CBA______6. ABC ADC ______

7. BAP BCP______8. SAT SAR ______

Given: BD bisects ABC

II.For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give the postulate that makes them congruent.

1.2. 3. Given: T is the midpoint of WR

a. ______a. ______a. ______

b. _____  _____b. _____  _____b. _____  _____

c. ______c. ______c. ______

4.5. Given: IH Bisects WIS6.

a. ______a. ______a. ______

b. _____  _____b. _____  _____b. _____  _____

c. ______c. ______c. ______

7.8.9.

a. ______a. ______a. ______

b. _____  _____b. _____  _____b. _____  _____

c. ______c. ______c. ______

10. Given: I is the midpoint 11. 12.

of ME and SL

a. ______a. ______a. ______

b. _____  _____b. _____  _____b. _____  _____

c. ______c. ______c. ______

III.Using the given postulate, tell which parts of the pair of triangles should be shown congruent.

1.SAS2. ASA3. SSS

______ ______ ______ ______

4. AAS5. HL6. ASA

______ ______ ______ ______

For each problem below, write a two-column proof on a separate piece of paper.

I. Proving Triangles Congruent:

1. 5.

2.

3.6.

4.

II. Using CPCTC

7. 10.

8. 11.

9.

Review: Triangles and Triangle Congruence

You will need a separate piece of paper to show all your work. This review is not comprehensive; always be sure to go back through your old homework and quizzes.

I canwrite a congruency statement representing two congruent polygons

  1. Write a congruency statement for the two triangles at right.

I canidentify congruent parts of a polygon, given a congruency statement

  1. List ALL of the congruent parts if

I canuse algebra to find the side lengths and angle measures of congruent polygons

  1. Find p.
  1. Find x.

I canname the five ways to prove triangles are congruent

  1. Name the 5 ways to prove triangles congruent.

I canprove triangles are congruent

For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give the postulate that makes them congruent.

  1. Given: I is the midpoint

of ME and SL

I canmark pieces of a triangle congruent given how they are to be proved congruent

  1. What information is
    missing to use HL?
  1. What information is missing to use SAS?

IV. For which value(s) of x are the triangles congruent?

3. x = ______4. x = ______

5. x = ______

I canwrite a two-column proof over congruent triangles

  1. Complete and review ALL proofs on the proofs worksheet.