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Congruence Statement and Corresponding Parts of Triangles

This article explains how to write congruence statements for triangles and identify pairs of congruent corresponding parts. It also provides examples of finding congruent parts and using properties of congruent figures.

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Congruence Statement and Corresponding Parts of Triangles

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  1. 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

  2. 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 Use properties of congruent figures SOLUTION

  3. You know that∠ F Q. m F = mQ 68 = 6y + 8 68 = (6y + x) o o 10 = y EXAMPLE 2 Use properties of congruent figures

  4. PAINTING If you divide the wall into orange and blue sections along JK, will the sections of the wall be the same size and shape?Explain. From the diagram, A Cand D Bbecause all right angles are congruent. Also, by the Lines Perpendicular to a Transversal Theorem, AB DC. EXAMPLE 3 Show that figures are congruent SOLUTION

  5. The diagram shows AJ CK, KDJB, and DA BC. By the Reflexive Property, JK KJ. All corresponding parts are congruent, so AJKD CKJB. EXAMPLE 3 Show that figures are congruent Then, 1 4 and 2 3 by the Alternate Interior Angles Theorem. So, all pairs of corresponding angles are congruent.

  6. In the diagram at the right, ABGH CDEF. Identify all pairs of congruent corresponding parts. AB CD, BG DE, GH FE, HA FC A C, B D, G E, H F. for Examples 1, 2, and 3 GUIDED PRACTICE SOLUTION Corresponding sides: Corresponding angles:

  7. In the diagram at the right, ABGH CDEF. 2. Find the value ofxand findm H. (a) You know that H F (4x+ 5)° = 105° 4x = 100 x = 25 (b) You know that H F m H m F =105° for Examples 1, 2, and 3 GUIDED PRACTICE SOLUTION

  8. In the diagram at the right, ABGH CDEF. 3. Show thatPTS RTQ. PS QR, PT TR, ST TQand Similarly all angles are to each other, therefore all of the corresponding points of PTS are congruent to those of RTQ by the indicated markings, the Vertical Angle Theorem and the Alternate Interior Angle theorem. for Examples 1, 2, and 3 GUIDED PRACTICE SOLUTION In the given diagram

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