4.2 Apply  to Δ’ s. OBJECTIVES Name and label corresponding parts of congruent triangles.

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Presentation transcript:

4.2 Apply  to Δ’ s

OBJECTIVES Name and label corresponding parts of congruent triangles

 Δ’s Δ’s Δ’s Δ’s Triangles (actually, ALL geometric figures) that are the same shape and size are congruent. Each triangle has three sides and three angles. If all six of the corresponding parts are congruent then the triangles are congruent.

CPCTC CPCTC Corresponding Parts of Congruent Triangles are Congruent Be sure to label  Δs with proper mappings (i.e. if  D   L,  V   P,  W   M, DV  LP, VW  PM, and WD  ML, then we must write ΔDVW  ΔLPM)

EXAMPLE 1 Identify Congruent Parts Write a congruence statement for the triangles. Identify all pairs of congruent corresponding parts. SOLUTION The diagram indicates that JKL TSR. Corresponding sides JK TS KL SR LJ RT Corresponding angles J T, K  S, L R

EXAMPLE 2 Use Properties of Congruent Figures In the diagram, DEFG SPQR. Find the value of x. a. b. Find the value of y. SOLUTION You know that FG QR. a. FG = QR 12 = 2x – 4 16= 2x 8= x EXAMPLE 2

Use Properties of Congruent Figures b. You know that  F Q. m F= m Q 68 = (6y + x) 68= 6y = y EXAMPLE 2 (continued)

Theorem 4.3 – Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent. Abbreviation: If 2  s of one Δ are  to 2  s of another Δ, then third  s are .

ASSIGNMENT Pre-AP Geometry: Pgs #4 – 21, 26Pre-AP Geometry: Pgs #4 – 21, 26