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Understanding Congruent Triangles: Labeling and Identifying Parts

Learn how to name and label parts of congruent triangles, identify pairs of congruent corresponding parts, and write congruence statements. Practice with examples and the Third Angles Theorem. Assignment included.

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Understanding Congruent Triangles: Labeling and Identifying Parts

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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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