Name: ______________________________________ Class: ______________ Date: ____________

I can analyze and apply properties of triangle congruence and polygons.

Directions: Please complete the necessary problems to earn the maximum number of points according

to the chart below. Show all of your work clearly and neatly for credit- which will be earned based on

completion rather than correctness.

Lesson Practice problems

Options Required Points Points Earned

Lesson 1: Proving Triangle Congruence by SAS

1-19 18 points

Lesson 2: Equilateral and Isosceles Triangles

1-18 17 points

Lesson 3: Proving Triangle Congruence by SSS

1-14 18 points

Lesson 4: Proving Triangle Congruence by ASA and AAS

1-12 17 points

Unit 6 - Congruent Triangles Investigation 2: Triangle Congruency

Practice Problems

________/70 points

Name: ______________________________________ Class: ______________ Date: ____________

1. (1 point) What is an included angle?

2. (1 point) Complete the sentence:

If two sides and the included angle of one triangle are congruent to two sides and the included

angle of a second triangle, then ___________________________________________________.

(1 point each) In Exercises 3-6, name the included angle between the pair of sides given.

3. 𝐽𝐾 and 𝐾𝐿 4. 𝑃𝐾 and 𝐿𝐾

5. 𝐿𝑃 and 𝐿𝐾 6. 𝐽𝐿 and 𝐽𝐾

(2 points each) In Exercises 7-10, decide whether enough information is given to prove that the

triangles are congruent using the SAS Congruence Theorem. Explain why or why not.

7. 8.

Name: ______________________________________ Class: ______________ Date: ____________

9. 10.

(3 points each) In Exercises 11 and 12, write a proof (See Example 1).

11.

12.

(2 points each) In Exercises 13-16, use the given information to name two triangles that are congruent.

Explain your reasoning (See Example 2).

13.

Name: ______________________________________ Class: ______________ Date: ____________

14.

15.

16.

17. (2 points) Describe and correct the error in finding the value of x.

Name: ______________________________________ Class: ______________ Date: ____________

18. (1 point) What additional information do you need to prove that ∆𝑨𝑩𝑪 ≅ ∆𝑫𝑩𝑪?

19. (3 points) The Navajo rug is made of isosceles triangles. You know ∠B ≅ ∠D. Create a proof that

uses SAS Congruence Theorem to show that ∆ABC ≅ ∆CDE (See Example 3).

1. (1 point) Describe how to identify the vertex angle of an isosceles triangle.

2. (1 point) What is the relationship between the base angles of an isosceles triangle? Explain.

(1 point each) In Exercises 3-6, complete the statement. State which theorem you used. (See Example

1.)

3. If 𝐴𝐸 ≅ 𝐷𝐸, then ∠ _______ ≅ ∠ _______.

4. If 𝐴𝐵 ≅ 𝐸𝐵, then ∠ _______ ≅ ∠ _______.

5. If ∠D ≅ ∠CED, then _______ ≅ _______.

6. If ∠EBC ≅ ∠ECB, then _______ ≅ _______.

Name: ______________________________________ Class: ______________ Date: ____________

(1 point each) In Exercises 7-10, find the value of x.

7. 8.

9. 10.

11. (1 point) The dimensions of a sports pennant are given in a diagram. Find the values of x and y.

(2 points each) In Exercises 12-14, find the values of x and y. (See Example 2).

12.

13.

14.

Name: ______________________________________ Class: ______________ Date: ____________

15. (2 points) Describe and correct the error in finding the length of 𝑩𝑪.

16. (4 points) The diagram represents part of the exterior of the Bow Tower in Calgary, Alberta,

Canada. In the diagram, ∆ABD and ∆CBD are congruent equilateral triangles. (See Example 3).

a. Explain why ∆ABC is isosceles.

b. Explain why ∠BAE ≅ ∠BCE.

c. Show that ∆ABE and ∆CBE are congruent.

d. Find the measure of ∠BAE.

(3 points each) In Exercises 17 and 18, find the perimeter of the triangle.

17. 18.

Name: ______________________________________ Class: ______________ Date: ____________

1. (1 point) The side opposite the right angle is called the _______________ of the right triangle.

2. (2 points) Which triangle’s legs do NOT belong with the other three? Explain your reasoning.

(2 points each) In Exercises 3 and 4, decide whether enough information is given to prove that the

triangles are congruent using the SSS Congruence Theorem. Explain why or why not.

3. 4.

(2 points each) In Exercises 5 and 6, decide whether enough information is given to prove that the

triangles are congruent using the HL Congruence Theorem. Explain why or why not.

5. 6.

Name: ______________________________________ Class: ______________ Date: ____________

(2 points each) In Exercises 7-8, decide whether the congruence statement is true. Explain your

reasoning. (See Example 1)

7. 8.

(2 points each) In Exercises 9-10, determine whether the figure is stable. Explain your reasoning. (See

Example 2)

9. 10.

(2 points each) In Exercises 11-12, write a proof. (See Example 3)

11. 12.

Name: ______________________________________ Class: ______________ Date: ____________

13. (3 points) The distances between consecutive bases on a softball field are the same. The distance

from home plate to second base is the same as the distance from first base to third base. The angles

created at each base are 90 degrees. Prove ∆HFS ≅ ∆FST ≅ ∆STH. (See Example 4.)

14. (3 points) Use the given coordinates to determine whether ∆ABC ≅ ∆DEF.

A(-2, -2), B(4, -2), C(4, 6), D(5, 7), E(5, 1), F(13, 1)

1. (2 points) How are the AAS Congruence Theorem and the ASA Congruence Theorem similar?

How are they different?

2. (2 points) You know that a pair of triangles has two pairs of congruent corresponding angles.

What other information do you need to know to show that the triangles are congruent?

Name: ______________________________________ Class: ______________ Date: ____________

(2 points each) In Exercises 3 and 4, decide whether enough information is given to prove that the

triangles are congruent. If so, state the theorem you would use. (See Example 1)

3. 4.

(1 point each) In Exercises 5 and 6, state the third congruence statement that is needed to prove that

∆FGH ≅ ∆LMN using the given theorem.

5. Given 𝐺𝐻 ≅ 𝑀𝑁, ∠G ≅ ∠M, _______≅_______. (Use the AAS Congruence Theorem.)

6. Given 𝐹𝐺 ≅ 𝐿𝑀, ∠G ≅ ∠M, _______≅_______. (Use the AAS Congruence Theorem.)

(2 points each) In Exercises 7 and 8, decide whether you can use the given information to prove that

∆ABC ≅ ∆DEF. Explain your reasoning.

7. ∠A ≅ ∠D, ∠C ≅ ∠F, 𝐴𝐶 ≅ 𝐷𝐹

8. ∠C ≅ ∠F, 𝐴𝐵 ≅ 𝐷𝐸, 𝐵𝐶 ≅ 𝐸𝐹

Name: ______________________________________ Class: ______________ Date: ____________

(2 points each) In Exercises 9 and 10, prove that the triangles are congruent using the ASA Congruence

Theorem. (See Example 2.)

9. 10.

(2 points each) In Exercises 11 and 12, prove that the triangles are congruent using the AAS

Congruence Theorem. (See Example 3.)

11. 12.