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Congruent Figures

Congruent Figures. GEOMETRY LESSON 4-1. (For help, go to Algebra Review, page 30.). Solve each equation. 1. x + 6 = 25 2. x + 7 + 13 = 33 3. 5 x = 540 4. x + 10 = 2 x 5. For the triangle at the right, use the Triangle Angle-Sum Theorem to find the value of y. x = 19. x = 13.

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Congruent Figures

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  1. Congruent Figures GEOMETRY LESSON 4-1 (For help, go to Algebra Review, page 30.) Solve each equation. 1.x + 6 = 25 2.x + 7 + 13 = 33 3. 5x = 540 4.x + 10 = 2x 5. For the triangle at the right, use the Triangle Angle-Sum Theorem to find the value of y. x = 19 x = 13 x = 108 x = 10 y = 50 Check Skills You’ll Need 4-1

  2. Congruent Figures GEOMETRY LESSON 4-1 Geometric figures are congruent if they are the same size and shape. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides. Two polygons are congruent polygons if and only if their corresponding sides and corresponding angles are congruent. 4-1

  3. Helpful Hint When you write a statement such as ABCDEF, you are also stating which parts are congruent. Congruent Figures GEOMETRY LESSON 4-1 In a congruence statement, the order of the vertices indicates the corresponding parts. 4-1

  4. Angles: A QB TC J Sides: AB QT BC TJ AC QJ Congruent Figures GEOMETRY LESSON 4-1 Naming Congruent Parts ABCQTJ. List the congruent corresponding parts. List the corresponding vertices in the same order. List the corresponding sides in the same order. Quick Check 4-1

  5. Congruent Figures GEOMETRY LESSON 4-1 Using Congruent Polygons XYZKLM, mY = 67, and mM = 48. Find mX. Use the Triangle Angle-Sum Theorem and the definition of congruent polygons to find mX. mX + mY + mZ = 180 Triangle Angle-Sum Theorem mZ = mMCorresponding angles of congruent triangles that are congruent mZ = 48 Substitute 48 for mM. mX + 67 + 48 = 180 Substitute. mX + 115 = 180 Simplify. mX = 65 Subtract 115 from each side. Quick Check 4-1

  6. If ABCCDE, then BACDCE. The diagram above shows BACDEC, not DCE. Corresponding angles are not necessarily congruent, therefore you cannot conclude that ABCCDE. Congruent Figures GEOMETRY LESSON 4-1 Finding Congruent Triangles Can you conclude that ABCCDE in the figure below? List corresponding vertices in the same order. Quick Check 4-1

  7. Congruent Figures GEOMETRY LESSON 4-1 Theorem 4-1 4-1

  8. Examine the diagram, and list the congruent corresponding parts for CNG and DNG. a. CGDGGiven b. CNDNGiven c. GNGNReflexive Property of Congruence d. CDGiven e. CNGDNGRight angles are congruent. f. CGNDGN Third Angles Theorem g. CNGDNGDefinition of  triangles Congruent Figures GEOMETRY LESSON 4-1 Proving Triangles Congruent Show how you can conclude that CNGDNG. List statements and reasons. Congruent triangles have three congruent corresponding sides and three congruent corresponding angles. Quick Check 4-1

  9. H E S T, WA NO, AS OT, SH TE, WH NE; W N, A O, Sample: DFHZPR Sample: ABDCDB Sample: Two pairs of corresponding sides and two pairs of corresponding angles are given. C A because all right angles are congruent. BDBD by the Reflexive Property of . ABDCDB by the definition of congruent triangles. Congruent Figures GEOMETRY LESSON 4-1 In Exercises 1 and 2, quadrilateral WASH quadrilateral NOTE. 1. List the congruent corresponding parts. 2.mO = mT = 90 and mH = 36. Find mN. 3. Write a statement of triangle congruence.4. Write a statement of triangle congruence.5. Explain your reasoning in Exercise 4 above. 144 4-1

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