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Geometry Chapter 4 Review

Geometry Chapter 4 Review. Geometry Chapter 4 Review. Classify triangles by angles: 1. The measure of two angles are 35 and 55. Geometry Chapter 4 Review. Classify triangles by angles: 1. The measure of two angles are 35 and 55. 2. The measures of two angles are 70 and 50.

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Geometry Chapter 4 Review

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  1. Geometry Chapter 4 Review

  2. Geometry Chapter 4 Review Classify triangles by angles: 1. The measure of two angles are 35 and 55.

  3. Geometry Chapter 4 Review Classify triangles by angles: 1. The measure of two angles are 35 and 55. 2. The measures of two angles are 70 and 50.

  4. Geometry Chapter 4 Review Classify triangles by angles: 1. The measure of two angles are 35 and 55. 2. The measures of two angles are 70 and 50. 3. The measure of one acute angle of a right triangle is 3/2 the measure of the other acute angle. Find the measure of each acute angle.

  5. Geometry Chapter 4 Review Classify triangles by angles: 1. The measure of two angles are 35 and 55. 2. The measures of two angles are 70 and 50. 3. The measure of one acute angle of a right triangle is 3/2 the measure of the other acute angle. Find the measure of each acute angle. 4. ABC is isosceles with: AC = AB, AC = 4x - 2 AB = 2x + 6, BC = 3x - 1 Find BC.

  6. Geometry Chapter 4 Review Prove the 180 Theorem

  7. Geometry Chapter 4 Review THIRD ANGLE Theorem – If TWO Angles of one Triangle are CONGRUENT to TWO Angles of a second triangle, then the THIRD angles of the triangles ARE CONTRUENT.

  8. Geometry Chapter 4 Review EXTERIOR ANGLE Theorem – The measure of an EXTERIOR Angle of a Triangle is EQUAL to the SUM of the Measures of the TWO REMOTE Interior Angles.

  9. Geometry Chapter 4 Review Using the figure at the right, answer the following : If m  4 is 140, then m  2 = _______

  10. Geometry Chapter 4 Review Using the figure at the right, answer the following : If m  C = 72, then the m  1 = ________

  11. Geometry Chapter 4 Review Using the figure at the right, answer the following : If m  2 = 34, then m  4 = __________

  12. Geometry Chapter 4 Review Definition: COROLLARY A statement that can be easily proved using a theorem is called a COLOLLARY. • The ACUTE ANGLES of a right triangle • are COMPLEMENTARY. • There can be at mostone right or obtuse angle • in a triangle.

  13. Congruent TRIANGLES have • Congruent CORRESPONDING SIDES • Congruent CORRESPONDING Angles F C B D E A

  14. Congruent TRIANGLES have • Congruent CORRESPONDING SIDES • Congruent CORRESPONDING Angles The way you NAME the Triangle establishes the CORRESPONDENCE:

  15. SO, if ABC  FGH: Congruent Angles Congruent Sides Be sure to WRITE the LETTERS of VERTICES in the CORRECT ORDER when you write a  Statement.

  16. H Geometry Chapter 4 Review Y T Given: L G P Are these Triangles CONGRUENT?

  17. To Prove Triangles are CONGRUENT: • Prove CORRESPONDING Sides and • CORRESPONDING Angles are CONGRUENT • Prove COORESPONDING SIDES are CONGRUENT • (SSS) • Prove Two CORRESPONDING Angles and the • INCLUDED SIDE are CONGRUENT (ASA) • Prove Two CORRESPONDING Sides and the • INCLUDED ANGLE are CONGRUENT (SAS) • Prove Two CORRESPONDING Angles and a • NONIncluded Side are CONGRUENT (AAS)

  18. H Geometry Chapter 4 Review Y T Given: L G P Are these Triangles CONGRUENT?

  19. H Geometry Chapter 4 Review Y T Given: L G P Are these Triangles CONGRUENT?

  20. H Geometry Chapter 4 Review Y T Given: L G P Find:

  21. Geometry Chapter 4 Review Given: ST = 2x + 13 YZ = 4x + 5 TR = 3x - 1 Find ZX:

  22. Geometry Chapter 4 Review Given: P M T Prove: Q

  23. Triangle MNO is both equilateral and equiangular. Triangle PQR has 3 congruent sides, m P = 60 and m Q = 60. Is Triangle MNO  PQR?

  24. Geometry Ch 4 Review CPCTC THEOREM RECALL: 2 triangles are CONGRUENT, IF: Their CORRESPONDING Sides are Congruent AND Their CORRESPONDING Angles are Congruent.

  25. Geometry Ch 4 Review CPCTC THEOREM THEREFORE, it follows: IF -- two triangles can be proved Congruent, THEN -- Any pair of Corresponding sides or pair of Corresponding Angles are Congruent.

  26. Geometry Ch 4 Review CPCTC THEOREM This is abbreviated: Corresponding Parts of Congruent Triangles are Congruent. C P C T C

  27. Geometry Chapter 4 Review K U G T Y Given: H Prove:

  28. Geometry Ch 4 Review Example of CPCTC S R P Q Given: Prove:

  29. Geometry Ch 4 Review

  30. Geometry Ch 4 Review Another Example of Using CPCTC E 5 6 1 3 4 2 C B F Given: Prove:

  31. Geometry Ch 4 Review Yet ANOTHER Example D E C A B Given: Prove:

  32. Geometry Ch 4 Review FINAL CPCTC Example A B E C D Prove: Given:

  33. Geometry Ch 4 Review

  34. Geometry Ch 4 Review

  35. Geometry Ch 4 Review

  36. Geometry Ch 4 Review Prove:  PWQ  MRQ

  37. Geometry Ch 4 Review

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