4.3 Congruent Triangles We will… …name and label corresponding parts of congruent triangles. …identify congruence transformations.

Corresponding parts of congruent triangles Triangles that are the same size and shape are congruent triangles. Each triangle has three angles and three sides. If all six corresponding parts are congruent, then the triangles are congruent.

Corresponding parts of congruent triangles X Z Y A C B If ΔABC is congruent to ΔXYZ , then vertices of the two triangles correspond in the same order as the letter naming the triangles. ΔABC = ΔXYZ ~

Corresponding parts of congruent triangles X Z Y A C B ΔABC = ΔXYZ ~ This correspondence of vertices can be used to name the corresponding congruent sides and angles of the two triangles.

Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if their corresponding parts are congruent. CPCTC 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. Answer: Since corresponding parts of congruent triangles are congruent, Example 3-1a

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 Example 3-1c

Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric, and transitive. REFLEXIVE ΔJKL = ΔJKL K K ~ L L J J

Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric, and transitive. SYMMETRIC ~ If ΔJKL = ΔPQR, then ΔPQR = ΔJKL. K Q L ~ R J P

Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric, and transitive. TRANSITIVE ~ If ΔJKL = ΔPQR, and ΔPQR = ΔXYZ, then ΔJKL = ΔXYZ. ~ K Q ~ L R J Y P Z X

IDENTIFY CONGRUENCE TRANSFORMATIONS If you slide ΔABC down and to the right, it is still congruent to ΔDEF. B E D F C A B A C

IDENTIFY CONGRUENCE TRANSFORMATIONS If you turn ΔABC, it is still congruent to ΔDEF. A B A C B C E D F

IDENTIFY CONGRUENCE TRANSFORMATIONS If you flip ΔABC, it is still congruent to ΔDEF. B A C E D F A C B

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. Example 3-2a

Use the Distance Formula to find the length of each side of the triangles. Example 3-2b

Use the Distance Formula to find the length of each side of the triangles. Example 3-2b

Use the Distance Formula to find the length of each side of the triangles. Example 3-2b

TempCopy 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 , Example 3-2c

Answer: RST is a turn of RST. 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. Example 3-2d

a. Verify that ABC ABC. 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. Example 3-2f

b. Name the congruence transformation for ABC and ABC. Answer: turn Example 3-2g

BOOKWORK: p. 195 #9 – 19, #22 – 25 (just name the congruence transformation) HOMEWORK: p.198 Practice Quiz