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Exploring Congruent Polygons: Lesson 4 Geometry

Learn to name and use corresponding parts of congruent polygons to prove triangles congruent. Explore the definition of congruence and appreciate the properties of congruent figures and polygons. Practice finding values of x and y using congruence statements.

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Exploring Congruent Polygons: Lesson 4 Geometry

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  1. Geometry Lesson 4 – 3 Congruent Triangles Objective: Name and use corresponding parts of congruent polygons. Prove triangles congruent using the definition of congruence.

  2. Congruent • Congruent • Figures that have exactly the same shape and size • Are the following congruent? Congruent, all same shape and size Not congruent, same shape, but not the same size.

  3. Congruent Polygons • Congruent Polygons • All parts are congruent (angles and sides) • Corresponding parts • Parts of the polygons that ‘match up’ • Two polygons are congruent if and only if their corresponding parts are congruent.

  4. Corresponding angles Congruence Statement Corresponding Sides Have to be in matching order

  5. Show that the polygons are congruent by identifying all the congruent corresponding parts. Then write a congruence statement. Congruence Statement:

  6. If and only if • If two polygons are congruent, then their corresponding parts are congruent. • Corresponding parts of congruent triangles are congruent • Abbreviation: CPCTC CPCTC can/will be used as a reason in proofs. NEED TO KNOW!

  7. Find the values of x and y. Use your congruence statement to match up parts. 8y – 5 = 99 8y = 104 y = 13 2y + x = 38.4 2(13) + x = 38.4 x = 12.4 26 + x = 38.4

  8. Find the values of x and y. 12 x = 12 2y – 1 = 24 2y = 25 y = 12.5

  9. Theorem 4.3 • Third Angle 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.

  10. The planners of the Senior Banquet decide to fold dinner napkins using the Triangle Pocket Fold so that they can place a small gift in the pocket.

  11. Theorem 4.4Properties of Triangle Congruence • Reflexive • Symmetric • Transitive

  12. Homework • Pg. 256 1 – 7 all, 10 – 20 E, 24, 58

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