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4.2 Apply  to Δ ’ s

4.2 Apply  to Δ ’ s. OBJECTIVES. Name and label corresponding parts of congruent triangles.  Δ ’ s. Triangles ( actually, ALL geometric figures) that are the same shape and size are congruent. Each triangle has three sides and three angles.

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4.2 Apply  to Δ ’ s

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  1. 4.2 Apply to Δ’s

  2. OBJECTIVES • Name and label corresponding parts of congruent triangles

  3. 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.

  4. 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)

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

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

  7. You know that∠ F Q. m F = mQ 68 = 6y + 8 68 = (6y + x) 10 = y EXAMPLE 2 (continued) EXAMPLE 2 Use Properties of Congruent Figures

  8. 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 .

  9. ASSIGNMENT • Pre-AP Geometry: Pgs. 228 - 231 #4 – 21, 26

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