Lesson 4-3

Congruent Triangles

5-Minute Check on Lesson 4-25-Minute Check on Lesson 4-25-Minute Check on Lesson 4-25-Minute Check on Lesson 4-2 Transparency 4-3

Find the measure of each angle.

1. m1

2. m2

3. m3

4. m4

5. m5

6. Two angles of a triangle measure 46 and 65. What is the measure of the third angle?Standardized Test Practice:

A CB D65 69 111 115

5-Minute Check on Lesson 4-25-Minute Check on Lesson 4-25-Minute Check on Lesson 4-25-Minute Check on Lesson 4-2 Transparency 4-3

Find the measure of each angle.

1. m1 115

2. m2 72

3. m3 57

4. m4 18

5. m5 122

6. Two angles of a triangle measure 46 and 65. What is the measure of the third angle?Standardized Test Practice:

A CB D65 69 111 115

Objectives

• Name and label corresponding parts of congruent triangles

• Identify congruence transformations

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)

Properties of Triangle Congruence

• Reflexive – ∆JKL ∆ JKL

• Symmetric – if ∆ JKL ∆ PQR, then ∆ PQR ∆ JKL

• Transitive – if ∆ JKL ∆ PQR and ∆ PQR ∆ XYZ, then ∆ JKL ∆ XYZ

Congruent Triangles

B

C

AX

Y

ZThe 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

Answer: Since corresponding parts of congruent triangles are congruent,

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.

Name the congruent triangles.

Answer: HIJ LIK

Answer:

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: ABC DEF

COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST are R(3, 0), S(0, ─5), and T(─1, ─1). Verify that RST RST.

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

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

Use a protractor to measure the angles of the triangles. You will find that the measures are the same.

Answer: The lengths of the corresponding sides of two triangles are equal. Therefore, by the definition of congruence,

In conclusion, because ,

COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST are R(3, 0), S(0, ─5), and T(─1, ─1). Name the congruence transformation for RST and RST.

Answer: RST is a turn of RST.

COORDINATE GEOMETRY The vertices of ABC are A(–5, 5), B(0, 3), and C(–4, 1). The vertices of ABC are A(5, –5), B(0, –3), and C(4, –1).

Answer:

Use a protractor to verify that corresponding angles are congruent.

a. Verify that ABC ABC.

Answer: turn

b. Name the congruence transformation for ABC and ABC.

Summary & Homework

• Summary:– Two triangles are congruent when all of

their corresponding parts are congruent.– Order is important!

• Homework: – pg 195-198: 9-12, 22-25, 40-42