1. Lesson 4-3
Congruent Triangles

2. Standardized Test Practice:
Transparency 4-3
5-Minute Check on Lesson 4-2
Find the measure of each angle.
1. m1
2. m2
3. m3
4. m4
5. m5
Two angles of a triangle measure 46 and 65. What is the measure of the third angle?
Standardized Test Practice: A
65 B
69 C
111 D
115

3. Standardized Test Practice:
Transparency 4-3
5-Minute Check on Lesson 4-2
Find the measure of each angle.
1. m1 115
2. m2 72
3. m3 57
4. m4 18
5. m5 122
Two angles of a triangle measure 46 and 65. What is the measure of the third angle?
Standardized Test Practice: A
65 B
69 C
111 D
115

4. Objectives Name and label corresponding parts of congruent triangles
Identify congruence transformations

5. Vocabulary
Congruent triangles – have the same size and shape (corresponding angles and sides )
Congruence Transformations:
Slide (also known as a translation)
Turn (also known as a rotation)
Flip (also known as a reflection)

6. Properties of Triangle Congruence
Reflexive – ∆JKL  ∆ JKL
Symmetric – if ∆ JKL  ∆ PQR, then ∆ PQR  ∆ JKL
Transitive – if ∆ JKL  ∆ PQR and ∆ PQR  ∆ XYZ, then ∆ JKL  ∆ XYZ

7. CPCTC – Corresponding Parts of Congruent Triangles are CongruentX A C Y B Z
The vertices of the two triangles correspond in the same order as the letters naming the triangle
▲ABC  ▲XYZ
A  X B  Y C  Z
AB  XY BC  YZ CA  ZX
CPCTC – Corresponding Parts of Congruent Triangles are Congruent

8. ARCHITECTURE A tower roof is composed of congruent triangles all converging toward a point at the top.
Name the corresponding congruent angles and sides of HIJ and LIK.
Answer: Since corresponding parts of congruent triangles are congruent,
Name the congruent triangles.
Answer: HIJ LIK

9. The support beams on the fence form congruent triangles.
b. Name the congruent triangles.
a. Name the corresponding congruent angles and sides of ABC and DEF.
Answer:
Answer: ABC DEF

10. COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST are R(3, 0), S(0, ─5), and T(─1, ─1). Verify that RST  RST.
Use the Distance Formula to find the length of each side of the triangles.

11. Use the Distance Formula to find the length of each side of the triangles.

12. Answer: The lengths of the corresponding sides of two triangles are equal. Therefore, by the definition of congruence,
Use a protractor to measure the angles of the triangles. You will find that the measures are the same.
In conclusion, because ,

13. COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST  are R(3, 0), S(0, ─5), and T(─1, ─1). Name the congruence transformation for RST and RST.
Answer: RST is a turn of RST.

14. COORDINATE GEOMETRY The vertices of ABC are A(–5, 5), B(0, 3), and C(–4, 1). The vertices of ABC are A(5, –5), B(0, –3), and C(4, –1).
a. Verify that ABC ABC.
Answer:
Use a protractor to verify that corresponding angles are congruent.
b. Name the congruence transformation for ABC and ABC.
Answer: turn

15. Summary & Homework Summary: Homework:
Two triangles are congruent when all of their corresponding parts are congruent.
Order is important!
Homework:
pg : 9-12, 22-25, 40-42