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Chapter 4- Part 2

Chapter 4- Part 2. Congruent Triangles. CPCTC (4-4). Definition of Congruent Triangles C orresponding P arts of C ongruent T riangles are C ongruent. Using Congruent Triangles: CPCTC. CPCTC – Corresponding parts of congruent triangles are congruent. DEF ≅ DGF by _____

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Chapter 4- Part 2

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  1. Chapter 4- Part 2 Congruent Triangles

  2. CPCTC (4-4) • Definition of Congruent Triangles • Corresponding • Parts of • Congruent • Triangles are • Congruent

  3. Using Congruent Triangles: CPCTC • CPCTC – Corresponding parts of congruent triangles are congruent. DEF ≅ DGF by _____ What other parts are congruent by CPCTC?

  4. Using Congruent Triangles: CPCTC ACE ≅ BDE by _________ What other parts are congruent by CPCTC?

  5. Class work • 4-3 Part 1 worksheet (complete in groups)

  6. Homework • 4-4 Practice worksheet #1-5

  7. Homework • p. 246-247 #6, 7, 9, 10, and 16 (proofs using CPCTC)

  8. Triangle Paper Activity (5 minutes!) • Fold paper in half and crease the fold • Cut off a corner (not on the creased side) to make a triangle. • Open the triangle and lay it flat. • Label the triangle vertices P, R, and S and the bottom of the fold Q. • Measure the lengths of the sides of the triangle using a ruler and measure the angles using a protractor. Record your measurements on the triangle. • Compare the lengths of the sides and the angle measures. Identify angle pairs and side pairs that are congruent. • Write a conjecture (if… then…) regarding your findings.

  9. Isosceles Triangles (4-5) Parts of an Isosceles Triangle • Base • Legs • Vertex Angle • Base Angles

  10. Isosceles Triangles (4-5) Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Converse of Isosceles Triangle Theorem If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

  11. Triangle Paper Activity • Using the same triangle as previously, • Draw a line down the crease of the triangle. • Measure <PRQ and <SRQ. Compare these measurements. • Measure <PQR and <SQR. Compare these measurements. • Find PQ and QS using a ruler. • Compare these two angle pairs and lengths of sides with other students’ pairs of angles and lengths of sides. Do you notice a pattern? • Write a conjecture (conclusion based on observations). Write your conjecture as an “if-then” conditional statement.

  12. Isosceles Triangles (4-5) Corollary: The bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. In other words, the bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.

  13. Isosceles Triangles (4-4) Find the values of x and y.

  14. Equilateral Triangles (4-5) Corollaries involving equilateral triangles: • If a triangle is equilateral, then the triangle is equiangular. • If a triangle is equiangular, then the triangle is equilateral.

  15. Classwork • 4-4 Handout (part 1)

  16. Homework • Isosceles and Equilateral Triangles worksheet

  17. Right Triangle Congruence (4-6) Hypotenuse-Leg (HL) Theorem If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

  18. Summary of Ways to Prove Two Triangles are Congruent

  19. Example

  20. Class work • Right Triangle Congruence worksheet • Review answers in ~15 minutes!

  21. Homework • 4-5 Other Methods of Proving Triangles Congruent worksheet (1-5 all)

  22. Section 4-7 Using More Than One Pair of Congruent Triangles Given: Prove: TU TW How many triangles do you see here? Which two triangles can we first prove are congruent?

  23. StatementsReasons Given 2. Reflexive ASA 4. CPCTC Reflexive SAS 7. CPCTC

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